CP-Algorithms Library

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:heavy_check_mark: Convolution (Mod $2^{64}$) (verify/poly/convolution64.test.cpp)

Depends on

Code

// @brief Convolution (Mod $2^{64}$)
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_2_64"
#pragma GCC optimize("Ofast,unroll-loops")
#define CP_ALGO_CHECKPOINT
#include <bits/stdc++.h>
#include "cp-algo/math/fft64.hpp"
#include "blazingio/blazingio.min.hpp"

using namespace std;

void solve() {
    int n, m;
    cin >> n >> m;
    vector<uint64_t, cp_algo::big_alloc<uint64_t>> a(n), b(m);
    for(auto &x : a) cin >> x;
    for(auto &x : b) cin >> x;
    cp_algo::checkpoint("read");
    cp_algo::math::fft::conv64(a, b);
    for(auto x: a) {
        cout << uint64_t(x) << " ";
    }
    cp_algo::checkpoint("write");
    cp_algo::checkpoint<1>();
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    solve();
}
#line 1 "verify/poly/convolution64.test.cpp"
// @brief Convolution (Mod $2^{64}$)
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_2_64"
#pragma GCC optimize("Ofast,unroll-loops")
#define CP_ALGO_CHECKPOINT
#include <bits/stdc++.h>
#line 1 "cp-algo/math/fft64.hpp"


#line 1 "cp-algo/random/rng.hpp"


#line 5 "cp-algo/random/rng.hpp"
namespace cp_algo::random {
    uint64_t rng() {
        static std::mt19937_64 rng(
            std::chrono::steady_clock::now().time_since_epoch().count()
        );
        return rng();
    }
}

#line 1 "cp-algo/math/common.hpp"


#line 6 "cp-algo/math/common.hpp"
namespace cp_algo::math {
#ifdef CP_ALGO_MAXN
    const int maxn = CP_ALGO_MAXN;
#else
    const int maxn = 1 << 19;
#endif
    const int magic = 64; // threshold for sizes to run the naive algo

    auto bpow(auto const& x, auto n, auto const& one, auto op) {
        if(n == 0) {
            return one;
        } else {
            auto t = bpow(x, n / 2, one, op);
            t = op(t, t);
            if(n % 2) {
                t = op(t, x);
            }
            return t;
        }
    }
    auto bpow(auto x, auto n, auto ans) {
        return bpow(x, n, ans, std::multiplies{});
    }
    template<typename T>
    T bpow(T const& x, auto n) {
        return bpow(x, n, T(1));
    }
    inline constexpr auto inv2(auto x) {
        assert(x % 2);
        std::make_unsigned_t<decltype(x)> y = 1;
        while(y * x != 1) {
            y *= 2 - x * y;
        }
        return y;
    }
}

#line 1 "cp-algo/math/cvector.hpp"


#line 1 "cp-algo/util/simd.hpp"


#include <experimental/simd>
#line 7 "cp-algo/util/simd.hpp"
namespace cp_algo {
    template<typename T, size_t len>
    using simd [[gnu::vector_size(len * sizeof(T))]] = T;
    using i64x4 = simd<int64_t, 4>;
    using u64x4 = simd<uint64_t, 4>;
    using u32x8 = simd<uint32_t, 8>;
    using i32x4 = simd<int32_t, 4>;
    using u32x4 = simd<uint32_t, 4>;
    using i16x4 = simd<int16_t, 4>;
    using u8x32 = simd<uint8_t, 32>;
    using dx4 = simd<double, 4>;

    [[gnu::target("avx2")]] inline dx4 abs(dx4 a) {
    return a < 0 ? -a : a;
    }

    // https://stackoverflow.com/a/77376595
    // works for ints in (-2^51, 2^51)
    static constexpr dx4 magic = dx4() + (3ULL << 51);
    [[gnu::target("avx2")]] inline i64x4 lround(dx4 x) {
        return i64x4(x + magic) - i64x4(magic);
    }
    [[gnu::target("avx2")]] inline dx4 to_double(i64x4 x) {
        return dx4(x + i64x4(magic)) - magic;
    }

    [[gnu::target("avx2")]] inline dx4 round(dx4 a) {
        return dx4{
            std::nearbyint(a[0]),
            std::nearbyint(a[1]),
            std::nearbyint(a[2]),
            std::nearbyint(a[3])
        };
    }

    [[gnu::target("avx2")]] inline u64x4 low32(u64x4 x) {
        return x & uint32_t(-1);
    }
    [[gnu::target("avx2")]] inline auto swap_bytes(auto x) {
        return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
    }
    [[gnu::target("avx2")]] inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
        auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
        x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
        return swap_bytes(x);
    }

    [[gnu::target("avx2")]] inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
        return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
    }
    [[gnu::target("avx2")]] inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
        return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
               u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
    }
    [[gnu::target("avx2")]] inline dx4 rotate_right(dx4 x) {
        static constexpr u64x4 shuffler = {3, 0, 1, 2};
        return __builtin_shuffle(x, shuffler);
    }

    template<std::size_t Align = 32>
    [[gnu::target("avx2")]] inline bool is_aligned(const auto* p) noexcept {
        return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
    }

    template<class Target>
    [[gnu::target("avx2")]] inline Target& vector_cast(auto &&p) {
        return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
    }
}

#line 1 "cp-algo/util/complex.hpp"


#line 5 "cp-algo/util/complex.hpp"
namespace cp_algo {
    // Custom implementation, since std::complex is UB on non-floating types
    template<typename T>
    struct complex {
        using value_type = T;
        T x, y;
        constexpr complex(): x(), y() {}
        constexpr complex(T x): x(x), y() {}
        constexpr complex(T x, T y): x(x), y(y) {}
        complex& operator *= (T t) {x *= t; y *= t; return *this;}
        complex& operator /= (T t) {x /= t; y /= t; return *this;}
        complex operator * (T t) const {return complex(*this) *= t;}
        complex operator / (T t) const {return complex(*this) /= t;}
        complex& operator += (complex t) {x += t.x; y += t.y; return *this;}
        complex& operator -= (complex t) {x -= t.x; y -= t.y; return *this;}
        complex operator * (complex t) const {return {x * t.x - y * t.y, x * t.y + y * t.x};}
        complex operator / (complex t) const {return *this * t.conj() / t.norm();}
        complex operator + (complex t) const {return complex(*this) += t;}
        complex operator - (complex t) const {return complex(*this) -= t;}
        complex& operator *= (complex t) {return *this = *this * t;}
        complex& operator /= (complex t) {return *this = *this / t;}
        complex operator - () const {return {-x, -y};}
        complex conj() const {return {x, -y};}
        T norm() const {return x * x + y * y;}
        T abs() const {return std::sqrt(norm());}
        T const real() const {return x;}
        T const imag() const {return y;}
        T& real() {return x;}
        T& imag() {return y;}
        static constexpr complex polar(T r, T theta) {return {T(r * cos(theta)), T(r * sin(theta))};}
        auto operator <=> (complex const& t) const = default;
    };
    template<typename T>
    complex<T> operator * (auto x, complex<T> y) {return y *= x;}
    template<typename T> complex<T> conj(complex<T> x) {return x.conj();}
    template<typename T> T norm(complex<T> x) {return x.norm();}
    template<typename T> T abs(complex<T> x) {return x.abs();}
    template<typename T> T& real(complex<T> &x) {return x.real();}
    template<typename T> T& imag(complex<T> &x) {return x.imag();}
    template<typename T> T const real(complex<T> const& x) {return x.real();}
    template<typename T> T const imag(complex<T> const& x) {return x.imag();}
    template<typename T>
    constexpr complex<T> polar(T r, T theta) {
        return complex<T>::polar(r, theta);
    }
    template<typename T>
    std::ostream& operator << (std::ostream &out, complex<T> x) {
        return out << x.real() << ' ' << x.imag();
    }
}

#line 1 "cp-algo/util/checkpoint.hpp"


#line 7 "cp-algo/util/checkpoint.hpp"
namespace cp_algo {
    std::map<std::string, double> checkpoints;
    template<bool final = false>
    void checkpoint([[maybe_unused]] std::string const& msg = "") {
#ifdef CP_ALGO_CHECKPOINT
        static double last = 0;
        double now = (double)clock() / CLOCKS_PER_SEC;
        double delta = now - last;
        last = now;
        if(msg.size() && !final) {
            checkpoints[msg] += delta;
        }
        if(final) {
            for(auto const& [key, value] : checkpoints) {
                std::cerr << key << ": " << value * 1000 << " ms\n";
            }
            std::cerr << "Total: " << now * 1000 << " ms\n";
        }
#endif
    }
}

#line 1 "cp-algo/util/big_alloc.hpp"



#line 6 "cp-algo/util/big_alloc.hpp"

// Single macro to detect POSIX platforms (Linux, Unix, macOS)
#if defined(__linux__) || defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
#  define CP_ALGO_USE_MMAP 1
#  include <sys/mman.h>
#else
#  define CP_ALGO_USE_MMAP 0
#endif

namespace cp_algo {
    template <typename T, std::size_t Align = 32>
    class big_alloc {
        static_assert( Align >= alignof(void*), "Align must be at least pointer-size");
        static_assert(std::popcount(Align) == 1, "Align must be a power of two");
    public:
        using value_type = T;
        template <class U> struct rebind { using other = big_alloc<U, Align>; };
        constexpr bool operator==(const big_alloc&) const = default;
        constexpr bool operator!=(const big_alloc&) const = default;

        big_alloc() noexcept = default;
        template <typename U, std::size_t A>
        big_alloc(const big_alloc<U, A>&) noexcept {}

        [[nodiscard]] T* allocate(std::size_t n) {
            std::size_t padded = round_up(n * sizeof(T));
            std::size_t align = std::max<std::size_t>(alignof(T),  Align);
#if CP_ALGO_USE_MMAP
            if (padded >= MEGABYTE) {
                void* raw = mmap(nullptr, padded,
                                PROT_READ | PROT_WRITE,
                                MAP_PRIVATE | MAP_ANONYMOUS, -1, 0);
                madvise(raw, padded, MADV_HUGEPAGE);
                madvise(raw, padded, MADV_POPULATE_WRITE);
                return static_cast<T*>(raw);
            }
#endif
            return static_cast<T*>(::operator new(padded, std::align_val_t(align)));
        }

        void deallocate(T* p, std::size_t n) noexcept {
            if (!p) return;
            std::size_t padded = round_up(n * sizeof(T));
            std::size_t align  = std::max<std::size_t>(alignof(T),  Align);
    #if CP_ALGO_USE_MMAP
            if (padded >= MEGABYTE) { munmap(p, padded); return; }
    #endif
            ::operator delete(p, padded, std::align_val_t(align));
        }

    private:
        static constexpr std::size_t MEGABYTE = 1 << 20;
        static constexpr std::size_t round_up(std::size_t x) noexcept {
            return (x + Align - 1) / Align * Align;
        }
    };
}

#line 7 "cp-algo/math/cvector.hpp"
#include <ranges>
#include <bit>

namespace stdx = std::experimental;
namespace cp_algo::math::fft {
    static constexpr size_t flen = 4;
    using ftype = double;
    using vftype = dx4;
    using point = complex<ftype>;
    using vpoint = complex<vftype>;
    static constexpr vftype vz = {};
    vpoint vi(vpoint const& r) {
        return {-imag(r), real(r)};
    }

    struct cvector {
        std::vector<vpoint, big_alloc<vpoint>> r;
        cvector(size_t n) {
            n = std::max(flen, std::bit_ceil(n));
            r.resize(n / flen);
            checkpoint("cvector create");
        }

        vpoint& at(size_t k) {return r[k / flen];}
        vpoint at(size_t k) const {return r[k / flen];}
        template<class pt = point>
        void set(size_t k, pt t) {
            if constexpr(std::is_same_v<pt, point>) {
                real(r[k / flen])[k % flen] = real(t);
                imag(r[k / flen])[k % flen] = imag(t);
            } else {
                at(k) = t;
            }
        }
        template<class pt = point>
        pt get(size_t k) const {
            if constexpr(std::is_same_v<pt, point>) {
                return {real(r[k / flen])[k % flen], imag(r[k / flen])[k % flen]};
            } else {
                return at(k);
            }
        }

        size_t size() const {
            return flen * r.size();
        }
        static constexpr size_t eval_arg(size_t n) {
            if(n < pre_evals) {
                return eval_args[n];
            } else {
                return eval_arg(n / 2) | (n & 1) << (std::bit_width(n) - 1);
            }
        }
        static constexpr point eval_point(size_t n) {
            if(n % 2) {
                return -eval_point(n - 1);
            } else if(n % 4) {
                return eval_point(n - 2) * point(0, 1);
            } else if(n / 4 < pre_evals) {
                return evalp[n / 4];
            } else {
                return polar<ftype>(1., std::numbers::pi / (ftype)std::bit_floor(n) * (ftype)eval_arg(n));
            }
        }
        static constexpr std::array<point, 32> roots = []() {
            std::array<point, 32> res;
            for(size_t i = 2; i < 32; i++) {
                res[i] = polar<ftype>(1., std::numbers::pi / (1ull << (i - 2)));
            }
            return res;
        }();
        static constexpr point root(size_t n) {
            return roots[std::bit_width(n)];
        }
        template<int step>
        static void exec_on_eval(size_t n, size_t k, auto &&callback) {
            callback(k, root(4 * step * n) * eval_point(step * k));
        }
        template<int step>
        static void exec_on_evals(size_t n, auto &&callback) {
            point factor = root(4 * step * n);
            for(size_t i = 0; i < n; i++) {
                callback(i, factor * eval_point(step * i));
            }
        }

        void dot(cvector const& t) {
            size_t n = this->size();
            exec_on_evals<1>(n / flen, [&](size_t k, point rt) {
                k *= flen;
                auto [Ax, Ay] = at(k);
                auto Bv = t.at(k);
                vpoint res = vz;
                for (size_t i = 0; i < flen; i++) {
                    res += vpoint(vz + Ax[i], vz + Ay[i]) * Bv;
                    real(Bv) = rotate_right(real(Bv));
                    imag(Bv) = rotate_right(imag(Bv));
                    auto x = real(Bv)[0], y = imag(Bv)[0];
                    real(Bv)[0] = x * real(rt) - y * imag(rt);
                    imag(Bv)[0] = x * imag(rt) + y * real(rt);
                }
                set(k, res);
            });
            checkpoint("dot");
        }
        template<bool partial = true>
        void ifft() {
            size_t n = size();
            if constexpr (!partial) {
                point pi(0, 1);
                exec_on_evals<4>(n / 4, [&](size_t k, point rt) {
                    k *= 4;
                    point v1 = conj(rt);
                    point v2 = v1 * v1;
                    point v3 = v1 * v2;
                    auto A = get(k);
                    auto B = get(k + 1);
                    auto C = get(k + 2);
                    auto D = get(k + 3);
                    set(k, (A + B) + (C + D));
                    set(k + 2, ((A + B) - (C + D)) * v2);
                    set(k + 1, ((A - B) - pi * (C - D)) * v1);
                    set(k + 3, ((A - B) + pi * (C - D)) * v3);
                });
            }
            bool parity = std::countr_zero(n) % 2;
            if(parity) {
                exec_on_evals<2>(n / (2 * flen), [&](size_t k, point rt) {
                    k *= 2 * flen;
                    vpoint cvrt = {vz + real(rt), vz - imag(rt)};
                    auto B = at(k) - at(k + flen);
                    at(k) += at(k + flen);
                    at(k + flen) = B * cvrt;
                });
            }

            for(size_t leaf = 3 * flen; leaf < n; leaf += 4 * flen) {
                size_t level = std::countr_one(leaf + 3);
                for(size_t lvl = 4 + parity; lvl <= level; lvl += 2) {
                    size_t i = (1 << lvl) / 4;
                    exec_on_eval<4>(n >> lvl, leaf >> lvl, [&](size_t k, point rt) {
                        k <<= lvl;
                        vpoint v1 = {vz + real(rt), vz - imag(rt)};
                        vpoint v2 = v1 * v1;
                        vpoint v3 = v1 * v2;
                        for(size_t j = k; j < k + i; j += flen) {
                            auto A = at(j);
                            auto B = at(j + i);
                            auto C = at(j + 2 * i);
                            auto D = at(j + 3 * i);
                            at(j) = ((A + B) + (C + D));
                            at(j + 2 * i) = ((A + B) - (C + D)) * v2;
                            at(j +     i) = ((A - B) - vi(C - D)) * v1;
                            at(j + 3 * i) = ((A - B) + vi(C - D)) * v3;
                        }
                    });
                }
            }
            checkpoint("ifft");
            for(size_t k = 0; k < n; k += flen) {
                if constexpr (partial) {
                    set(k, get<vpoint>(k) /= vz + ftype(n / flen));
                } else {
                    set(k, get<vpoint>(k) /= vz + ftype(n));
                }
            }
        }
        template<bool partial = true>
        void fft() {
            size_t n = size();
            bool parity = std::countr_zero(n) % 2;
            for(size_t leaf = 0; leaf < n; leaf += 4 * flen) {
                size_t level = std::countr_zero(n + leaf);
                level -= level % 2 != parity;
                for(size_t lvl = level; lvl >= 4; lvl -= 2) {
                    size_t i = (1 << lvl) / 4;
                    exec_on_eval<4>(n >> lvl, leaf >> lvl, [&](size_t k, point rt) {
                        k <<= lvl;
                        vpoint v1 = {vz + real(rt), vz + imag(rt)};
                        vpoint v2 = v1 * v1;
                        vpoint v3 = v1 * v2;
                        for(size_t j = k; j < k + i; j += flen) {
                            auto A = at(j);
                            auto B = at(j + i) * v1;
                            auto C = at(j + 2 * i) * v2;
                            auto D = at(j + 3 * i) * v3;
                            at(j)         = (A + C) + (B + D);
                            at(j + i)     = (A + C) - (B + D);
                            at(j + 2 * i) = (A - C) + vi(B - D);
                            at(j + 3 * i) = (A - C) - vi(B - D);
                        }
                    });
                }
            }
            if(parity) {
                exec_on_evals<2>(n / (2 * flen), [&](size_t k, point rt) {
                    k *= 2 * flen;
                    vpoint vrt = {vz + real(rt), vz + imag(rt)};
                    auto t = at(k + flen) * vrt;
                    at(k + flen) = at(k) - t;
                    at(k) += t;
                });
            }
            if constexpr (!partial) {
                point pi(0, 1);
                exec_on_evals<4>(n / 4, [&](size_t k, point rt) {
                    k *= 4;
                    point v1 = rt;
                    point v2 = v1 * v1;
                    point v3 = v1 * v2;
                        auto A = get(k);
                        auto B = get(k + 1) * v1;
                        auto C = get(k + 2) * v2;
                        auto D = get(k + 3) * v3;
                        set(k, (A + C) + (B + D));
                        set(k + 1, (A + C) - (B + D));
                        set(k + 2, (A - C) + pi * (B - D));
                        set(k + 3, (A - C) - pi * (B - D));
                });
            }
            checkpoint("fft");
        }
        static constexpr size_t pre_evals = 1 << 16;
        static const std::array<size_t, pre_evals> eval_args;
        static const std::array<point, pre_evals> evalp;
    };

    const std::array<size_t, cvector::pre_evals> cvector::eval_args = []() {
        std::array<size_t, pre_evals> res = {};
        for(size_t i = 1; i < pre_evals; i++) {
            res[i] = res[i >> 1] | (i & 1) << (std::bit_width(i) - 1);
        }
        return res;
    }();
    const std::array<point, cvector::pre_evals> cvector::evalp = []() {
        std::array<point, pre_evals> res = {};
        res[0] = 1;
        for(size_t n = 1; n < pre_evals; n++) {
            res[n] = polar<ftype>(1., std::numbers::pi * ftype(eval_args[n]) / ftype(4 * std::bit_floor(n)));
        }
        return res;
    }();
}

#line 6 "cp-algo/math/fft64.hpp"

namespace cp_algo::math::fft {
    struct dft64 {
        std::vector<cp_algo::math::fft::cvector> cv;

        static uint64_t factor, ifactor;
        static bool _init;

        static void init() {
            if(_init) return;
            _init = true;
            factor = random::rng();
            if(factor % 2 == 0) {factor++;}
            ifactor = inv2(factor);
        }

        dft64(auto const& a, size_t n): cv(4, n) {
            init();
            uint64_t cur = 1, step = bpow(factor, n);
            for(size_t i = 0; i < std::min(std::size(a), n); i++) {
                auto split = [&](size_t i, uint64_t mul) -> std::array<int16_t, 4> {
                    uint64_t x = i < std::size(a) ? a[i] * mul : 0;
                    std::array<int16_t, 4> res;
                    for(int z = 0; z < 4; z++) {
                        res[z] = int16_t(x);
                        x = (x >> 16) + (res[z] < 0);
                    }
                    return res;
                };
                auto re = split(i, cur);
                auto im = split(n + i, cur * step);
                for(int z = 0; z < 4; z++) {
                    real(cv[z].at(i))[i % 4] = re[z];
                    imag(cv[z].at(i))[i % 4] = im[z];
                }
                cur *= factor;
            }
            checkpoint("dft64 init");
            for(auto &x: cv) {
                x.fft();
            }
        }

        void dot(dft64 const& t) {
            size_t N = cv[0].size();
            cvector::exec_on_evals<1>(N / flen, [&](size_t k, point rt) {
                k *= flen;
                auto [A0x, A0y] = cv[0].at(k);
                auto [A1x, A1y] = cv[1].at(k);
                auto [A2x, A2y] = cv[2].at(k);
                auto [A3x, A3y] = cv[3].at(k);
                std::array B = {
                    t.cv[0].at(k),
                    t.cv[1].at(k),
                    t.cv[2].at(k),
                    t.cv[3].at(k)
                };

                std::array<vpoint, 4> C = {vz, vz, vz, vz};
                for (size_t i = 0; i < flen; i++) {
                    std::array A = {
                        vpoint{vz + A0x[i], vz + A0y[i]},
                        vpoint{vz + A1x[i], vz + A1y[i]},
                        vpoint{vz + A2x[i], vz + A2y[i]},
                        vpoint{vz + A3x[i], vz + A3y[i]}
                    };
                    for(size_t k = 0; k < 4; k++) {
                        for(size_t i = 0; i <= k; i++) {
                            C[k] += A[i] * B[k - i];
                        }
                    }
                    for(size_t k = 0; k < 4; k++) {
                        real(B[k]) = rotate_right(real(B[k]));
                        imag(B[k]) = rotate_right(imag(B[k]));
                        auto bx = real(B[k])[0], by = imag(B[k])[0];
                        real(B[k])[0] = bx * real(rt) - by * imag(rt);
                        imag(B[k])[0] = bx * imag(rt) + by * real(rt);
                    }
                }
                cv[0].at(k) = C[0];
                cv[1].at(k) = C[1];
                cv[2].at(k) = C[2];
                cv[3].at(k) = C[3];
            });
            checkpoint("dot");
            for(auto &x: cv) {
                x.ifft();
            }
        }

        void recover_mod(auto &res, size_t k) {
            size_t n = cv[0].size();
            uint64_t cur = 1, step = bpow(ifactor, n);
            for(size_t i = 0; i < std::min(k, n); i++) {
                std::array re = {real(cv[0].get(i)), real(cv[1].get(i)), real(cv[2].get(i)), real(cv[3].get(i))};
                std::array im = {imag(cv[0].get(i)), imag(cv[1].get(i)), imag(cv[2].get(i)), imag(cv[3].get(i))};
                auto set_i = [&](size_t i, auto &x, auto mul) {
                    if (i >= k) return;
                    res[i] = llround(x[0]) + (llround(x[1]) << 16) + (llround(x[2]) << 32) + (llround(x[3]) << 48);
                    res[i] *= mul;
                };
                set_i(i, re, cur);
                set_i(n + i, im, cur * step);
                cur *= ifactor;
            }
            cp_algo::checkpoint("recover mod");
        }
    };
    uint64_t dft64::factor = 1, dft64::ifactor = 1;
    bool dft64::_init = false;

    void conv64(auto& a, auto const& b) {
        size_t n = a.size(), m = b.size();
        size_t N = std::max(flen, std::bit_ceil(n + m - 1) / 2);
        dft64 A(a, N), B(b, N);
        A.dot(B);
        a.resize(n + m - 1);
        A.recover_mod(a, n + m - 1);
    }
}

#line 1 "blazingio/blazingio.min.hpp"
// NOLINTBEGIN
// clang-format off
// DO NOT REMOVE THIS MESSAGE. The mess that follows is a minified build of
// https://github.com/purplesyringa/blazingio. Refer to the repository for
// a human-readable version and documentation.
// Options: cbfoiedrhWLMXaIaAn
#define M$(x,...)_mm256_##x##_epi8(__VA_ARGS__)
#define $u(...)__VA_ARGS__
#if __APPLE__
#define $m(A,B)A
#else
#define $m(A,B)B
#endif
#if _WIN32
#define $w(A,B)A
#else
#define $w(A,B)B
#endif
#if __i386__|_M_IX86
#define $H(A,B)A
#else
#define $H(A,B)B
#endif
#if __aarch64__
#define $a(A,B)A
#else
#define $a(A,B)B
#endif
#define $P(x)void F(x K){
#define $T template<$c T
#define $c class
#define $C constexpr
#define $R return
#define $O operator
#define u$ uint64_t
#define $r $R*this;
#line 41 "blazingio/blazingio.min.hpp"
#include $a(<arm_neon.h>,<immintrin.h>)
#line 43 "blazingio/blazingio.min.hpp"
#include $w(<windows.h>,<sys/mman.h>)
#include<sys/stat.h>
#include $w(<io.h>,<unistd.h>)
#include $w(<ios>,<sys/resource.h>)
#if _MSC_VER
#define __builtin_add_overflow(a,b,c)_addcarry_u64(0,a,b,c)
#define $s
#else
$H(,u$ _umul128(u$ a,u$ b,u$*D){auto x=(__uint128_t)a*b;*D=u$(x>>64);$R(u$)x;})
#define $s $a(,__attribute__((target("avx2"))))
#endif
#define $z $a(16,32)
#define $t $a(uint8x16_t,__m256i)
#define $I $w(__forceinline,__attribute__((always_inline)))
#define $F M(),
#define E$(x)if(!(x))abort();
$w(LONG WINAPI $x(_EXCEPTION_POINTERS*);,)namespace $f{using namespace std;struct B{enum $c A:char{}c;B&$O=(char x){c=A{x};$r}$O char(){$R(char)c;}};$C u$ C=~0ULL/255;struct D{string&K;};static B E[65568];template<int F>struct G{B*H,*S;void K(off_t C){$w(char*D=(char*)VirtualAlloc(0,(C+8191)&-4096,8192,1);E$(D)E$(VirtualFree(D,0,32768))DWORD A=C&-65536;E$(!A||MapViewOfFileEx(CreateFileMapping(GetStdHandle(-10),0,2,0,A,0),4,0,0,0,D)==D)E$(VirtualAlloc(D+A,65536,12288,4)==D+A)E$(~_lseek(0,A,0))DWORD E=0;ReadFile(GetStdHandle(-10),D+A,65536,&E,0);,int A=getpagesize();char*D=(char*)mmap(0,C+A,3,2,0,0);E$(D!=(void*)-1)E$(mmap(D+((C+A-1)&-A),A,3,$m(4114,50),-1,0)!=(void*)-1))H=(B*)D+C;*H=10;H[1]=48;H[2]=0;S=(B*)D;}void L(){H=S=E;}$I void M(){if(F&&S==H){$w(DWORD A=0;ReadFile(GetStdHandle(-10),S=E,65536,&A,0);,$a($u(register long A asm("x0")=0,D asm("x1")=(long)E,G asm("x2")=65536,C asm($m("x16","x8"))=$m(3,63);asm volatile("svc 0" $m("x80",):"+r"(A),"+r"(D):"r"(C),"r"(G));S=launder(E);),off_t A=$H(3,$m(33554435,0));B*D=E;asm volatile($H("int $128","syscall"):"+a"(A),$H("+c"(D):"b","+S"(D):"D")(0),"d"(65536)$H(,$u(:"rcx","r11")));S=D;))H=S+A;*H=10;if(!A)E[1]=48,E[2]=0;}}$T>$I void N(T&x){while($F(*S&240)==48)x=T(x*10+(*S++-48));}$T>$I decltype((void)~T{1})O(T&x){M();int A=is_signed_v<T>&&*S==45;S+=A;N(x=0);x=A?1+~x:x;}$T>$I decltype((void)T{1.})O(T&x){M();int A=*S==45;S+=A;$F S+=*S==43;u$ n=0;int i=0;for(;i<18&&($F*S&240)==48;i++)n=n*10+*S++-48;int B=20;int C=*S==46;S+=C;for(;i<18&&($F*S&240)==48;i++)n=n*10+*S++-48,B-=C;x=(T)n;while(($F*S&240)==48)x=x*10+*S++-48,B-=C;if(*S==46)S++,C=1;while(($F*S&240)==48)x=x*10+*S++-48,B-=C;int D;if((*S|32)==101)S++,$F S+=*S==43,O(D),B+=D;static $C auto E=[](){array<T,41>E{};T x=1;for(int i=21;i--;)E[40-i]=x,E[i]=1/x,x*=10;$R E;}();while(B>40)x*=(T)1e10,B-=10;while(B<0)x*=(T)1e-10,B+=10;x*=E[B];x=A?-x:x;}$I void O(bool&x){$F x=*S++==49;}$I void O(char&x){$F x=*S++;}$I void O(uint8_t&x){$F x=*S++;}$I void O(int8_t&x){$F x=*S++;}$T>$s void P(string&K,T C){M();B*G=S;C();K.assign((char*)G,S-G);while(F&&S==H&&($F H!=E)){C();K.append(E,S);}}$s void O(string&K){P(K,[&]()$s{B*p=S;$w(ULONG R;,)$t x;$a(uint64x2_t A;while(memcpy(&x,p,16),A=uint64x2_t(x<33),!(A[0]|A[1]))p+=16;S=p+(A[0]?0:8)+$w((_BitScanForward64(&R,A[0]?A[0]:A[1]),R),__builtin_ctzll(A[0]?A[0]:A[1]))/8;,int J;$t C=M$(set1,32);while(memcpy(&x,p,32),!(J=M$(movemask,M$(cmpeq,C,_mm256_max_epu8(C,x)))))p+=32;S=p+$w((_BitScanForward(&R,J),R),__builtin_ctz(J));)});}$s void O(D&A){P(A.K,[&](){S=(B*)memchr(S,10,H-S+1);});if(A.K.size()&&A.K.back()==13)A.K.pop_back();if(A.K.empty()||S<H)S+=*S==10;}$T>$I void O(complex<T>&K){T A,B{};if($F*S==40){S++;O(A);if($F*S++==44)Q(B),S++;}else O(A);K={A,B};}template<size_t N>$s void O(bitset<N>&K){if(N>4095&&!*this)$R;ptrdiff_t i=N;while(i)if($F i%$z||H-S<$z)K[--i]=*S++==49;else{B*p=S;for(int64_t j=0;j<min(i,H-S)/$z;j++){i-=$z;$t x;memcpy(&x,p,$z);$a(auto B=(uint8x16_t)vdupq_n_u64(~2ULL/254)&(48-x);auto C=vzip_u8(vget_high_u8(B),vget_low_u8(B));auto y=vaddvq_u16((uint16x8_t)vcombine_u8(C.val[0],C.val[1]));,u$ a=~0ULL/65025;auto y=$w(_byteswap_ulong,__builtin_bswap32)(M$(movemask,M$(shuffle,_mm256_slli_epi32(x,7),_mm256_set_epi64x(a+C*24,a+C*16,a+C*8,a))));)p+=$z;memcpy((char*)&K+i/8,&y,$z/8);}S=p;}}$T>$I void Q(T&K){if(!is_same_v<T,D>)while($F(uint8_t)*S<33)S++;O(K);}$O bool(){$R!!*this;}bool $O!(){$R S>H;}};struct U{G<0>A;G<1>B;U(){struct stat D;E$(~fstat(0,&D))(D.st_mode>>12)==8?A.K(D.st_size):B.L();}U*tie(nullptr_t){$R this;}void sync_with_stdio(bool){}$T>$I U&$O>>(T&K){A.S?A.Q(K):B.Q(K);$r}$O bool(){$R!!*this;}bool $O!(){$R A.S?!A:!B;}};short A[100];char L[64]{1};struct
V{char*D;B*S;int J;V(){$w(E$(D=(char*)VirtualAlloc(0,536870912,8192,4))E$(VirtualAlloc(D,4096,4096,260))AddVectoredExceptionHandler(1,$x);,size_t C=536870912;$m(,rlimit E;getrlimit(RLIMIT_AS,&E);if(~E.rlim_cur)C=25165824;)D=(char*)mmap(0,C,3,$m(4162,16418),-1,0);E$(D!=(void*)-1))S=(B*)D;for(int i=0;i<100;i++)A[i]=short((48+i/10)|((48+i%10)<<8));for(int i=1;i<64;i++)L[i]=L[i-1]+(0x8922489224892249>>i&1);}~V(){flush($w(!J,));}void flush($w(int F=0,)){$w(J=1;auto E=GetStdHandle(-11);auto C=F?ReOpenFile(E,1073741824,7,2684354560):(void*)-1;DWORD A;E$(C==(void*)-1?WriteFile(E,D,DWORD((char*)S-D),&A,0):(WriteFile(C,D,DWORD(((char*)S-D+4095)&-4096),&A,0)&&~_chsize(1,int((char*)S-D)))),auto G=D;ssize_t A;while((A=write(1,G,(char*)S-G))>0)G+=A;E$(~A))S=(B*)D;}$P(char)*S++=K;}$P(uint8_t)*S++=K;}$P(int8_t)*S++=K;}$P(bool)*S++=48+K;}$T>decltype((void)~T{1})F(T K){using D=make_unsigned_t<T>;D C=K;if(K<0)F('-'),C=1+~C;static $C auto N=[](){array<D,5*sizeof(T)/2>N{};D n=1;for(size_t i=1;i<N.size();i++)n*=10,N[i]=n;$R N;}();$w(ULONG M;,)int G=L[$w(($H(_BitScanReverse(&M,ULONG((int64_t)C>>32))?M+=32:_BitScanReverse(&M,(ULONG)C|1),_BitScanReverse64(&M,C|1)),M),63^__builtin_clzll(C|1))];G-=C<N[G-1];short H[20];if $C(sizeof(T)==2){auto n=33555U*C-C/2;u$ H=A[n>>25];n=(n&33554431)*25;H|=A[n>>23]<<16;H|=u$(48+((n&8388607)*5>>22))<<32;H>>=40-G*8;memcpy(S,&H,8);}else if $C(sizeof(T)==4){auto n=1441151881ULL*C;$H(n>>=25;n++;for(int i=0;i<5;i++){H[i]=A[n>>32];n=(n&~0U)*100;},int K=57;auto J=~0ULL>>7;for(int i=0;i<5;i++){H[i]=A[n>>K];n=(n&J)*25;K-=2;J/=4;})memcpy(S,(B*)H+10-G,16);}else{$H($u(if(C<(1ULL<<32)){$R F((uint32_t)C);}auto J=(u$)1e10;auto x=C/J,y=C%J;int K=100000,b[]{int(x/K),int(x%K),int(y/K),int(y%K)};B H[40];for(int i=0;i<4;i++){int n=int((429497ULL*b[i]>>7)+1);B*p=H+i*5;*p=48+char(n>>25);n=(n&~0U>>7)*25;memcpy(p+1,A+(n>>23),2);memcpy(p+3,A+((n&~0U>>9)*25>>21),2);}),$u(u$ D,E=_umul128(18,C,&D),F;_umul128(0x725dd1d243aba0e8,C,&F);D+=__builtin_add_overflow(E,F+1,&E);for(int i=0;i<10;i++)H[i]=A[D],E=_umul128(100,E,&D);))memcpy(S,(B*)H+20-G,20);}S+=G;}$T>decltype((void)T{1.})F(T K){if(K<0)F('-'),K=-K;auto G=[&](){auto x=u$(K*1e12);$H($u(x-=x>999999999999;uint32_t n[]{uint32_t(x/1000000*429497>>7)+1,uint32_t(x%1000000*429497>>7)+1};int K=25,J=~0U>>7;for(int i=0;i<3;i++){for(int j=0;j<2;j++)memcpy(S+i*2+j*6,A+(n[j]>>K),2),n[j]=(n[j]&J)*25;K-=2;J/=4;}S+=12;),$u(u$ D,E=_umul128(472236648287,x,&D)>>8;E|=D<<56;D>>=8;E++;for(int i=0;i<6;i++)memcpy(S,A+D,2),S+=2,E=_umul128(100,E,&D);))};if(K==0)$R F('0');if(K>=1e16){K*=(T)1e-16;int B=16;while(K>=1)K*=(T).1,B++;F("0.");G();F('e');F(B);}else if(K>=1){auto B=(u$)K;F(B);if((K-=(T)B)>0)F('.'),G();}else F("0."),G();}$P(const char*)$w(size_t A=strlen(K);memcpy((char*)S,K,A);S+=A;,S=(B*)stpcpy((char*)S,K);)}$P(const uint8_t*)F((char*)K);}$P(const int8_t*)F((char*)K);}$P(string_view)memcpy(S,K.data(),K.size());S+=K.size();}$T>$P(complex<T>)*this<<'('<<K.real()<<','<<K.imag()<<')';}template<size_t N>$s $P(const bitset<N>&)auto i=N;while(i%$z)*S++=48+K[--i];B*p=S;while(i){i-=$z;$a(short,int)x;memcpy(&x,(char*)&K+i/8,$z/8);$a(auto A=(uint8x8_t)vdup_n_u16(x);vst1q_u8((uint8_t*)p,48-vtstq_u8(vcombine_u8(vuzp2_u8(A,A),vuzp1_u8(A,A)),(uint8x16_t)vdupq_n_u64(~2ULL/254)));,auto b=_mm256_set1_epi64x(~2ULL/254);_mm256_storeu_si256(($t*)p,M$(sub,M$(set1,48),M$(cmpeq,_mm256_and_si256(M$(shuffle,_mm256_set1_epi32(x),_mm256_set_epi64x(0,C,C*2,C*3)),b),b)));)p+=$z;}S=p;}$T>V&$O<<(const T&K){F(K);$r}V&$O<<(V&(*A)(V&)){$R A(*this);}};struct W{$T>W&$O<<(const T&K){$r}W&$O<<(W&(*A)(W&)){$R A(*this);}};}namespace std{$f::U i$;$f::V o$;$f::W e$;$f::U&getline($f::U&B,string&K){$f::D A{K};$R B>>A;}$f::V&flush($f::V&B){if(!i$.A.S)B.flush();$R B;}$f::V&endl($f::V&B){$R B<<'\n'<<flush;}$f::W&endl($f::W&B){$R B;}$f::W&flush($f::W&B){$R B;}}$w(LONG WINAPI $x(_EXCEPTION_POINTERS*A){auto C=A->ExceptionRecord;auto B=C->ExceptionInformation[1];if(C->ExceptionCode==2147483649&&B-(ULONG_PTR)std::o$.D<0x40000000){E$(VirtualAlloc((char*)B,16777216,4096,4)&&VirtualAlloc((char*)(B+16777216),4096,4096,260))$R-1;}$R 0;},)
#define freopen(...)if(freopen(__VA_ARGS__)==stdin)std::i$=$f::U{}
#define cin i$
#define cout o$
#ifdef ONLINE_JUDGE
#define cerr e$
#define clog e$
#endif
// End of blazingio
// NOLINTEND
// clang-format on
#line 8 "verify/poly/convolution64.test.cpp"

using namespace std;

void solve() {
    int n, m;
    cin >> n >> m;
    vector<uint64_t, cp_algo::big_alloc<uint64_t>> a(n), b(m);
    for(auto &x : a) cin >> x;
    for(auto &x : b) cin >> x;
    cp_algo::checkpoint("read");
    cp_algo::math::fft::conv64(a, b);
    for(auto x: a) {
        cout << uint64_t(x) << " ";
    }
    cp_algo::checkpoint("write");
    cp_algo::checkpoint<1>();
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    solve();
}

Test cases

Env Name Status Elapsed Memory
g++ all_same_00 :heavy_check_mark: AC 81 ms 88 MB
g++ all_same_01 :heavy_check_mark: AC 108 ms 107 MB
g++ all_same_02 :heavy_check_mark: AC 103 ms 107 MB
g++ all_same_03 :heavy_check_mark: AC 112 ms 107 MB
g++ example_00 :heavy_check_mark: AC 5 ms 6 MB
g++ example_01 :heavy_check_mark: AC 5 ms 6 MB
g++ gen_131072_00 :heavy_check_mark: AC 31 ms 29 MB
g++ gen_131073_00 :heavy_check_mark: AC 42 ms 48 MB
g++ gen_177147_00 :heavy_check_mark: AC 47 ms 50 MB
g++ gen_177148_00 :heavy_check_mark: AC 47 ms 50 MB
g++ gen_262144_00 :heavy_check_mark: AC 55 ms 55 MB
g++ gen_262145_00 :heavy_check_mark: AC 82 ms 92 MB
g++ gen_265721_00 :heavy_check_mark: AC 80 ms 92 MB
g++ gen_265722_00 :heavy_check_mark: AC 81 ms 92 MB
g++ gen_354294_00 :heavy_check_mark: AC 91 ms 97 MB
g++ gen_354295_00 :heavy_check_mark: AC 91 ms 97 MB
g++ gen_524288_00 :heavy_check_mark: AC 107 ms 107 MB
g++ gen_524288_01 :heavy_check_mark: AC 109 ms 107 MB
g++ medium_00 :heavy_check_mark: AC 7 ms 7 MB
g++ medium_01 :heavy_check_mark: AC 5 ms 7 MB
g++ medium_02 :heavy_check_mark: AC 6 ms 7 MB
g++ random_00 :heavy_check_mark: AC 95 ms 100 MB
g++ random_01 :heavy_check_mark: AC 94 ms 102 MB
g++ random_02 :heavy_check_mark: AC 51 ms 53 MB
g++ small_00 :heavy_check_mark: AC 5 ms 6 MB
g++ small_01 :heavy_check_mark: AC 5 ms 6 MB
g++ small_02 :heavy_check_mark: AC 5 ms 6 MB
g++ small_03 :heavy_check_mark: AC 5 ms 6 MB
g++ small_04 :heavy_check_mark: AC 5 ms 6 MB
g++ small_05 :heavy_check_mark: AC 5 ms 6 MB
g++ small_06 :heavy_check_mark: AC 5 ms 6 MB
g++ small_07 :heavy_check_mark: AC 5 ms 6 MB
g++ small_08 :heavy_check_mark: AC 5 ms 6 MB
g++ small_09 :heavy_check_mark: AC 5 ms 6 MB
g++ small_10 :heavy_check_mark: AC 5 ms 6 MB
g++ small_11 :heavy_check_mark: AC 5 ms 6 MB
g++ small_12 :heavy_check_mark: AC 5 ms 6 MB
g++ small_13 :heavy_check_mark: AC 5 ms 6 MB
g++ small_14 :heavy_check_mark: AC 5 ms 6 MB
g++ small_15 :heavy_check_mark: AC 5 ms 6 MB
g++ small_and_large_00 :heavy_check_mark: AC 78 ms 92 MB
g++ small_and_large_01 :heavy_check_mark: AC 80 ms 92 MB
g++ small_and_large_02 :heavy_check_mark: AC 79 ms 92 MB
g++ small_and_large_03 :heavy_check_mark: AC 81 ms 92 MB
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