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:heavy_check_mark: cp-algo/number_theory/modint.hpp

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#ifndef CP_ALGO_NUMBER_THEORY_MODINT_HPP
#define CP_ALGO_NUMBER_THEORY_MODINT_HPP
#include "../math/common.hpp"
#include <iostream>
#include <cassert>
namespace cp_algo::math {

    template<typename modint, typename _Int>
    struct modint_base {
        using Int = _Int;
        using UInt = std::make_unsigned_t<Int>;
        static constexpr size_t bits = sizeof(Int) * 8;
        using Int2 = std::conditional_t<bits <= 32, int64_t, __int128_t>;
        using UInt2 = std::conditional_t<bits <= 32, uint64_t, __uint128_t>;
        constexpr static Int mod() {
            return modint::mod();
        }
        constexpr static UInt remod() {
            return modint::remod();
        }
        constexpr static UInt2 modmod() {
            return UInt2(mod()) * mod();
        }
        constexpr modint_base() = default;
        constexpr modint_base(Int2 rr) {
            to_modint().setr(UInt((rr + modmod()) % mod()));
        }
        constexpr modint inv() const {
            return bpow(to_modint(), mod() - 2);
        }
        modint operator-() const {
            modint neg;
            neg.r = std::min(-r, remod() - r);
            return neg;
        }
        modint& operator/=(const modint& t) {
            return to_modint() *= t.inv();
        }
        modint& operator*=(const modint& t) {
            r = UInt(UInt2(r) * t.r % mod());
            return to_modint();
        }
        modint& operator+=(const modint& t) {
            r += t.r;
            r = std::min(r, r - remod());
            return to_modint();
        }
        modint& operator-=(const modint& t) {
            r -= t.r;
            r = std::min(r, r + remod());
            return to_modint();
        }
        modint operator+(const modint& t) const { return modint(to_modint()) += t; }
        modint operator-(const modint& t) const { return modint(to_modint()) -= t; }
        modint operator*(const modint& t) const { return modint(to_modint()) *= t; }
        modint operator/(const modint& t) const { return modint(to_modint()) /= t; }
        // Why <=> doesn't work?..
        auto operator==(const modint& t) const { return to_modint().getr() == t.getr(); }
        auto operator!=(const modint& t) const { return to_modint().getr() != t.getr(); }
        auto operator<=(const modint& t) const { return to_modint().getr() <= t.getr(); }
        auto operator>=(const modint& t) const { return to_modint().getr() >= t.getr(); }
        auto operator<(const modint& t) const { return to_modint().getr() < t.getr(); }
        auto operator>(const modint& t) const { return to_modint().getr() > t.getr(); }
        Int rem() const {
            UInt R = to_modint().getr();
            return R - (R > (UInt)mod() / 2) * mod();
        }
        constexpr void setr(UInt rr) {
            r = rr;
        }
        constexpr UInt getr() const {
            return r;
        }

        // Only use these if you really know what you're doing!
        static uint64_t modmod8() { return uint64_t(8 * modmod()); }
        void add_unsafe(UInt t) { r += t; }
        void pseudonormalize() { r = std::min(r, r - modmod8()); }
        modint const& normalize() {
            if(r >= (UInt)mod()) {
                r %= mod();
            }
            return to_modint();
        }
        void setr_direct(UInt rr) { r = rr; }
        UInt getr_direct() const { return r; }

    protected:
        UInt r;

    private:
        constexpr modint& to_modint() { return static_cast<modint&>(*this); }
        constexpr modint const& to_modint() const { return static_cast<modint const&>(*this); }
    };
    template<typename modint>
    concept modint_type = std::is_base_of_v<modint_base<modint, typename modint::Int>, modint>;
    template<modint_type modint>
    decltype(std::cin)& operator>>(decltype(std::cin)& in, modint& x) {
        typename modint::UInt r;
        auto &res = in >> r;
        x.setr(r);
        return res;
    }
    template<modint_type modint>
    decltype(std::cout)& operator<<(decltype(std::cout)& out, modint const& x) {
        return out << x.getr();
    }

    template<auto m>
    struct modint: modint_base<modint<m>, decltype(m)> {
        using Base = modint_base<modint<m>, decltype(m)>;
        using Base::Base;
        static constexpr Base::Int mod() { return m; }
        static constexpr Base::UInt remod() { return m; }
        auto getr() const { return Base::r; }
    };

    // Odd moduli up to a quarter of the unsigned word keep Montgomery residues lazily in
    // [0, 2 mod): remod() = 2 mod, and both 4 mod and ab + q * mod fit. Any other modulus keeps
    // fully reduced residues, remod() = mod, which is what the sums of modint_base need then:
    // an even one without the Montgomery form, a wide odd one with a reduction that subtracts
    // high words instead of adding double words that would overflow.
    template<typename Int = int>
    struct dynamic_modint: modint_base<dynamic_modint<Int>, Int> {
        using Base = modint_base<dynamic_modint<Int>, Int>;
        using Base::Base;

        // Out of line, so that the hot path stays as small as it was.
        [[gnu::noinline, gnu::cold]] static Base::UInt m_reduce_reduced(Base::UInt2 ab) {
            if(mod() % 2 == 0) {
                return typename Base::UInt(ab % mod());
            }
            // q * mod has the low word of ab, so the difference of the high words is exact.
            typename Base::UInt q = -(typename Base::UInt(ab) * inverse);
            auto high = typename Base::UInt(ab >> Base::bits);
            auto low = typename Base::UInt(typename Base::UInt2(q) * typename Base::UInt(mod()) >> Base::bits);
            return high >= low ? high - low : high - low + mod();
        }
        static Base::UInt m_reduce(Base::UInt2 ab) {
            if(imod() == 0) [[unlikely]] {
                return m_reduce_reduced(ab);
            }
            typename Base::UInt2 m = typename Base::UInt(ab) * imod();
            return typename Base::UInt((ab + m * mod()) >> Base::bits);
        }
        static Base::UInt m_transform(Base::UInt a) {
            if(mod() % 2 == 0) [[unlikely]] {
                return a;
            } else {
                return m_reduce(a * pw128());
            }
        }
        dynamic_modint& operator*=(const dynamic_modint& t) {
            Base::r = m_reduce(typename Base::UInt2(Base::r) * t.r);
            return *this;
        }
        void setr(Base::UInt rr) {
            Base::r = m_transform(rr);
        }
        Base::UInt getr() const {
            typename Base::UInt res = m_reduce(Base::r);
            return std::min(res, res - mod());
        }
        static Int mod() { return m; }
        static Base::UInt remod() { return rm; }
        static Base::UInt imod() { return im; }
        static Base::UInt2 pw128() { return r2; }
        static void switch_mod(Int nm) {
            m = nm;
            bool lazy = m % 2 && typename Base::UInt(m) <= typename Base::UInt(-1) / 4;
            rm = typename Base::UInt(m) * (lazy ? 2 : 1);
            inverse = m % 2 ? inv2(-m) : 0;
            im = lazy ? inverse : 0;
            r2 = static_cast<Base::UInt>(static_cast<Base::UInt2>(-1) % m + 1);
        }

        // Wrapper for temp switching
        auto static with_mod(Int tmp, auto callback) {
            struct scoped {
                Int prev = mod();
                ~scoped() { switch_mod(prev); }
            } _;
            switch_mod(tmp);
            return callback();
        }

    private:
        static inline thread_local Int m = 1;
        // im: -1 / mod modulo 2^bits for lazy residues and 0 for reduced ones; inverse: the same
        // for every odd mod; rm: the value of remod().
        static inline thread_local Base::UInt im = -1, r2 = 0, inverse = -1, rm = 2;
    };
}
#endif // CP_ALGO_MATH_MODINT_HPP

#line 1 "cp-algo/number_theory/modint.hpp"


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


#include <functional>
#include <cstdint>
#include <cassert>
#include <bit>
#include <vector>
#include <algorithm>
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

    // Nonnegative 64-bit exponents, with an associative operation and its identity.
    // Windows >1 precompute odd powers only when that saves operations.
    template<int window = 1>
    auto bpow(auto const& x, auto n, auto const& one, auto op) {
        static_assert(window >= 1 && window <= 6);
        if constexpr(window > 1) {
            if(n == 0) {return one;}
            int bits = std::bit_width(uint64_t(n));
            auto low_bit = [&](int high) {
                int low = std::max(0, high - window + 1);
                while(!((n >> low) & 1)) {low++;}
                return low;
            };
            int first = low_bit(bits - 1);
            int cost = (1 << (window - 1)) + first;
            for(int j = first - 1; j >= 0;) {
                if(!((n >> j) & 1)) {j--;}
                else {cost++; j = low_bit(j) - 1;}
            }
            // Do not pay for the table when binary powering uses fewer operations.
            if(cost >= bits + std::popcount(uint64_t(n)) - 2) {return bpow<1>(x, n, one, op);}
            using T = std::decay_t<decltype(x)>;
            std::vector<T> odd;
            odd.reserve(1 << (window - 1));
            odd.push_back(x);
            auto square = op(x, x);
            while(odd.size() < size_t(1 << (window - 1))) {odd.push_back(op(odd.back(), square));}
            auto ans = odd[(n >> first) / 2];
            for(int j = first - 1; j >= 0;) {
                if(!((n >> j) & 1)) {ans = op(ans, ans); j--;}
                else {
                    int low = low_bit(j), length = j - low + 1;
                    auto digit = (n >> low) & ((1u << length) - 1);
                    for(int i = 0; i < length; i++) {ans = op(ans, ans);}
                    ans = op(ans, odd[digit / 2]);
                    j = low - 1;
                }
            }
            return ans;
        } else {
            if (n == 0) {
                return one;
            }
            auto ans = x;
            for(int j = std::bit_width<uint64_t>(n) - 2; ~j; j--) {
                ans = op(ans, ans);
                if((n >> j) & 1) {
                    ans = op(ans, x);
                }
            }
            return ans;
        }
    }
    template<int window = 1>
    auto bpow(auto x, auto n, auto ans) {
        return bpow<window>(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 4 "cp-algo/number_theory/modint.hpp"
#include <iostream>
#line 6 "cp-algo/number_theory/modint.hpp"
namespace cp_algo::math {

    template<typename modint, typename _Int>
    struct modint_base {
        using Int = _Int;
        using UInt = std::make_unsigned_t<Int>;
        static constexpr size_t bits = sizeof(Int) * 8;
        using Int2 = std::conditional_t<bits <= 32, int64_t, __int128_t>;
        using UInt2 = std::conditional_t<bits <= 32, uint64_t, __uint128_t>;
        constexpr static Int mod() {
            return modint::mod();
        }
        constexpr static UInt remod() {
            return modint::remod();
        }
        constexpr static UInt2 modmod() {
            return UInt2(mod()) * mod();
        }
        constexpr modint_base() = default;
        constexpr modint_base(Int2 rr) {
            to_modint().setr(UInt((rr + modmod()) % mod()));
        }
        constexpr modint inv() const {
            return bpow(to_modint(), mod() - 2);
        }
        modint operator-() const {
            modint neg;
            neg.r = std::min(-r, remod() - r);
            return neg;
        }
        modint& operator/=(const modint& t) {
            return to_modint() *= t.inv();
        }
        modint& operator*=(const modint& t) {
            r = UInt(UInt2(r) * t.r % mod());
            return to_modint();
        }
        modint& operator+=(const modint& t) {
            r += t.r;
            r = std::min(r, r - remod());
            return to_modint();
        }
        modint& operator-=(const modint& t) {
            r -= t.r;
            r = std::min(r, r + remod());
            return to_modint();
        }
        modint operator+(const modint& t) const { return modint(to_modint()) += t; }
        modint operator-(const modint& t) const { return modint(to_modint()) -= t; }
        modint operator*(const modint& t) const { return modint(to_modint()) *= t; }
        modint operator/(const modint& t) const { return modint(to_modint()) /= t; }
        // Why <=> doesn't work?..
        auto operator==(const modint& t) const { return to_modint().getr() == t.getr(); }
        auto operator!=(const modint& t) const { return to_modint().getr() != t.getr(); }
        auto operator<=(const modint& t) const { return to_modint().getr() <= t.getr(); }
        auto operator>=(const modint& t) const { return to_modint().getr() >= t.getr(); }
        auto operator<(const modint& t) const { return to_modint().getr() < t.getr(); }
        auto operator>(const modint& t) const { return to_modint().getr() > t.getr(); }
        Int rem() const {
            UInt R = to_modint().getr();
            return R - (R > (UInt)mod() / 2) * mod();
        }
        constexpr void setr(UInt rr) {
            r = rr;
        }
        constexpr UInt getr() const {
            return r;
        }

        // Only use these if you really know what you're doing!
        static uint64_t modmod8() { return uint64_t(8 * modmod()); }
        void add_unsafe(UInt t) { r += t; }
        void pseudonormalize() { r = std::min(r, r - modmod8()); }
        modint const& normalize() {
            if(r >= (UInt)mod()) {
                r %= mod();
            }
            return to_modint();
        }
        void setr_direct(UInt rr) { r = rr; }
        UInt getr_direct() const { return r; }

    protected:
        UInt r;

    private:
        constexpr modint& to_modint() { return static_cast<modint&>(*this); }
        constexpr modint const& to_modint() const { return static_cast<modint const&>(*this); }
    };
    template<typename modint>
    concept modint_type = std::is_base_of_v<modint_base<modint, typename modint::Int>, modint>;
    template<modint_type modint>
    decltype(std::cin)& operator>>(decltype(std::cin)& in, modint& x) {
        typename modint::UInt r;
        auto &res = in >> r;
        x.setr(r);
        return res;
    }
    template<modint_type modint>
    decltype(std::cout)& operator<<(decltype(std::cout)& out, modint const& x) {
        return out << x.getr();
    }

    template<auto m>
    struct modint: modint_base<modint<m>, decltype(m)> {
        using Base = modint_base<modint<m>, decltype(m)>;
        using Base::Base;
        static constexpr Base::Int mod() { return m; }
        static constexpr Base::UInt remod() { return m; }
        auto getr() const { return Base::r; }
    };

    // Odd moduli up to a quarter of the unsigned word keep Montgomery residues lazily in
    // [0, 2 mod): remod() = 2 mod, and both 4 mod and ab + q * mod fit. Any other modulus keeps
    // fully reduced residues, remod() = mod, which is what the sums of modint_base need then:
    // an even one without the Montgomery form, a wide odd one with a reduction that subtracts
    // high words instead of adding double words that would overflow.
    template<typename Int = int>
    struct dynamic_modint: modint_base<dynamic_modint<Int>, Int> {
        using Base = modint_base<dynamic_modint<Int>, Int>;
        using Base::Base;

        // Out of line, so that the hot path stays as small as it was.
        [[gnu::noinline, gnu::cold]] static Base::UInt m_reduce_reduced(Base::UInt2 ab) {
            if(mod() % 2 == 0) {
                return typename Base::UInt(ab % mod());
            }
            // q * mod has the low word of ab, so the difference of the high words is exact.
            typename Base::UInt q = -(typename Base::UInt(ab) * inverse);
            auto high = typename Base::UInt(ab >> Base::bits);
            auto low = typename Base::UInt(typename Base::UInt2(q) * typename Base::UInt(mod()) >> Base::bits);
            return high >= low ? high - low : high - low + mod();
        }
        static Base::UInt m_reduce(Base::UInt2 ab) {
            if(imod() == 0) [[unlikely]] {
                return m_reduce_reduced(ab);
            }
            typename Base::UInt2 m = typename Base::UInt(ab) * imod();
            return typename Base::UInt((ab + m * mod()) >> Base::bits);
        }
        static Base::UInt m_transform(Base::UInt a) {
            if(mod() % 2 == 0) [[unlikely]] {
                return a;
            } else {
                return m_reduce(a * pw128());
            }
        }
        dynamic_modint& operator*=(const dynamic_modint& t) {
            Base::r = m_reduce(typename Base::UInt2(Base::r) * t.r);
            return *this;
        }
        void setr(Base::UInt rr) {
            Base::r = m_transform(rr);
        }
        Base::UInt getr() const {
            typename Base::UInt res = m_reduce(Base::r);
            return std::min(res, res - mod());
        }
        static Int mod() { return m; }
        static Base::UInt remod() { return rm; }
        static Base::UInt imod() { return im; }
        static Base::UInt2 pw128() { return r2; }
        static void switch_mod(Int nm) {
            m = nm;
            bool lazy = m % 2 && typename Base::UInt(m) <= typename Base::UInt(-1) / 4;
            rm = typename Base::UInt(m) * (lazy ? 2 : 1);
            inverse = m % 2 ? inv2(-m) : 0;
            im = lazy ? inverse : 0;
            r2 = static_cast<Base::UInt>(static_cast<Base::UInt2>(-1) % m + 1);
        }

        // Wrapper for temp switching
        auto static with_mod(Int tmp, auto callback) {
            struct scoped {
                Int prev = mod();
                ~scoped() { switch_mod(prev); }
            } _;
            switch_mod(tmp);
            return callback();
        }

    private:
        static inline thread_local Int m = 1;
        // im: -1 / mod modulo 2^bits for lazy residues and 0 for reduced ones; inverse: the same
        // for every odd mod; rm: the value of remod().
        static inline thread_local Base::UInt im = -1, r2 = 0, inverse = -1, rm = 2;
    };
}


#ifndef CP_ALGO_NUMBER_THEORY_MODINT_HPP
#define CP_ALGO_NUMBER_THEORY_MODINT_HPP
#include "../math/common.hpp"
#include <iostream>
#include <cassert>
namespace cp_algo::math{ template<typename modint,typename _Int> struct modint_base{ using Int=_Int; using UInt=std::make_unsigned_t<Int>; static constexpr size_t bits=sizeof(Int)*8; using Int2=std::conditional_t<bits<=32,int64_t,__int128_t>; using UInt2=std::conditional_t<bits<=32,uint64_t,__uint128_t>; constexpr static Int mod(){ return modint::mod(); } constexpr static UInt remod(){ return modint::remod(); } constexpr static UInt2 modmod(){ return UInt2(mod())*mod(); } constexpr modint_base()=default; constexpr modint_base(Int2 rr){ to_modint().setr(UInt((rr+modmod())%mod())); } constexpr modint inv()const{ return bpow(to_modint(),mod()-2); } modint operator-()const{ modint neg; neg.r=std::min(-r,remod()-r); return neg; } modint&operator/=(const modint&t){ return to_modint()*=t.inv(); } modint&operator*=(const modint&t){ r=UInt(UInt2(r)*t.r%mod()); return to_modint(); } modint&operator+=(const modint&t){ r+=t.r; r=std::min(r,r-remod()); return to_modint(); } modint&operator-=(const modint&t){ r-=t.r; r=std::min(r,r+remod()); return to_modint(); } modint operator+(const modint&t)const{return modint(to_modint())+=t;} modint operator-(const modint&t)const{return modint(to_modint())-=t;} modint operator*(const modint&t)const{return modint(to_modint())*=t;} modint operator/(const modint&t)const{return modint(to_modint())/=t;} auto operator==(const modint&t)const{return to_modint().getr()==t.getr();} auto operator!=(const modint&t)const{return to_modint().getr()!=t.getr();} auto operator<=(const modint&t)const{return to_modint().getr()<=t.getr();} auto operator>=(const modint&t)const{return to_modint().getr()>=t.getr();} auto operator<(const modint&t)const{return to_modint().getr()<t.getr();} auto operator>(const modint&t)const{return to_modint().getr()>t.getr();} Int rem()const{ UInt R=to_modint().getr(); return R-(R>(UInt)mod()/2)*mod(); } constexpr void setr(UInt rr){ r=rr; } constexpr UInt getr()const{ return r; } static uint64_t modmod8(){return uint64_t(8*modmod());} void add_unsafe(UInt t){r+=t;} void pseudonormalize(){r=std::min(r,r-modmod8());} modint const&normalize(){ if(r>=(UInt)mod()){ r%=mod(); } return to_modint(); } void setr_direct(UInt rr){r=rr;} UInt getr_direct()const{return r;} protected: UInt r; private: constexpr modint&to_modint(){return static_cast<modint&>(*this);} constexpr modint const&to_modint()const{return static_cast<modint const&>(*this);} }; template<typename modint> concept modint_type=std::is_base_of_v<modint_base<modint,typename modint::Int>,modint>; template<modint_type modint> decltype(std::cin)&operator>>(decltype(std::cin)&in,modint&x){ typename modint::UInt r; auto&res=in>>r; x.setr(r); return res; } template<modint_type modint> decltype(std::cout)&operator<<(decltype(std::cout)&out,modint const&x){ return out<<x.getr(); } template<auto m> struct modint:modint_base<modint<m>,decltype(m)>{ using Base=modint_base<modint<m>,decltype(m)>; using Base::Base; static constexpr Base::Int mod(){return m;} static constexpr Base::UInt remod(){return m;} auto getr()const{return Base::r;} }; template<typename Int=int> struct dynamic_modint:modint_base<dynamic_modint<Int>,Int>{ using Base=modint_base<dynamic_modint<Int>,Int>; using Base::Base; [[gnu::noinline,gnu::cold]]static Base::UInt m_reduce_reduced(Base::UInt2 ab){ if(mod()%2==0){ return typename Base::UInt(ab%mod()); } typename Base::UInt q= -(typename Base::UInt(ab)*inverse); auto high=typename Base::UInt(ab>>Base::bits); auto low=typename Base::UInt(typename Base::UInt2(q)*typename Base::UInt(mod())>>Base::bits); return high>=low?high-low:high-low+mod(); } static Base::UInt m_reduce(Base::UInt2 ab){ if(imod()==0)[[unlikely]]{ return m_reduce_reduced(ab); } typename Base::UInt2 m=typename Base::UInt(ab)*imod(); return typename Base::UInt((ab+m*mod())>>Base::bits); } static Base::UInt m_transform(Base::UInt a){ if(mod()%2==0)[[unlikely]]{ return a; }else{ return m_reduce(a*pw128()); } } dynamic_modint&operator*=(const dynamic_modint&t){ Base::r=m_reduce(typename Base::UInt2(Base::r)*t.r); return*this; } void setr(Base::UInt rr){ Base::r=m_transform(rr); } Base::UInt getr()const{ typename Base::UInt res=m_reduce(Base::r); return std::min(res,res-mod()); } static Int mod(){return m;} static Base::UInt remod(){return rm;} static Base::UInt imod(){return im;} static Base::UInt2 pw128(){return r2;} static void switch_mod(Int nm){ m=nm; bool lazy=m%2&&typename Base::UInt(m)<=typename Base::UInt(-1)/4; rm=typename Base::UInt(m)*(lazy?2:1); inverse=m%2?inv2(-m):0; im=lazy?inverse:0; r2=static_cast<Base::UInt>(static_cast<Base::UInt2>(-1)%m+1); } auto static with_mod(Int tmp,auto callback){ struct scoped{ Int prev=mod(); ~scoped(){switch_mod(prev);} }_; switch_mod(tmp); return callback(); } private: static inline thread_local Int m=1; static inline thread_local Base::UInt im= -1,r2=0,inverse= -1,rm=2; }; }
#endif

#line 1 "cp-algo/number_theory/modint.hpp"
#line 1 "cp-algo/math/common.hpp"
#include <functional>
#include <cstdint>
#include <cassert>
#include <bit>
#include <vector>
#include <algorithm>
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; template<int window=1> auto bpow(auto const&x,auto n,auto const&one,auto op){ static_assert(window>=1&&window<=6); if constexpr(window>1){ if(n==0){return one;} int bits=std::bit_width(uint64_t(n)); auto low_bit= [&](int high){ int low=std::max(0,high-window+1); while(!((n>>low)&1)){low++;} return low; }; int first=low_bit(bits-1); int cost=(1<<(window-1))+first; for(int j=first-1;j>=0;){ if(!((n>>j)&1)){j--;} else{cost++;j=low_bit(j)-1;} } if(cost>=bits+std::popcount(uint64_t(n))-2){return bpow<1>(x,n,one,op);} using T=std::decay_t<decltype(x)>; std::vector<T>odd; odd.reserve(1<<(window-1)); odd.push_back(x); auto square=op(x,x); while(odd.size()<size_t(1<<(window-1))){odd.push_back(op(odd.back(),square));} auto ans=odd[(n>>first)/2]; for(int j=first-1;j>=0;){ if(!((n>>j)&1)){ans=op(ans,ans);j--;} else{ int low=low_bit(j),length=j-low+1; auto digit=(n>>low)&((1u<<length)-1); for(int i=0;i<length;i++){ans=op(ans,ans);} ans=op(ans,odd[digit/2]); j=low-1; } } return ans; }else{ if(n==0){ return one; } auto ans=x; for(int j=std::bit_width<uint64_t>(n)-2;~j;j--){ ans=op(ans,ans); if((n>>j)&1){ ans=op(ans,x); } } return ans; } } template<int window=1> auto bpow(auto x,auto n,auto ans){ return bpow<window>(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 4 "cp-algo/number_theory/modint.hpp"
#include <iostream>
#line 6 "cp-algo/number_theory/modint.hpp"
namespace cp_algo::math{ template<typename modint,typename _Int> struct modint_base{ using Int=_Int; using UInt=std::make_unsigned_t<Int>; static constexpr size_t bits=sizeof(Int)*8; using Int2=std::conditional_t<bits<=32,int64_t,__int128_t>; using UInt2=std::conditional_t<bits<=32,uint64_t,__uint128_t>; constexpr static Int mod(){ return modint::mod(); } constexpr static UInt remod(){ return modint::remod(); } constexpr static UInt2 modmod(){ return UInt2(mod())*mod(); } constexpr modint_base()=default; constexpr modint_base(Int2 rr){ to_modint().setr(UInt((rr+modmod())%mod())); } constexpr modint inv()const{ return bpow(to_modint(),mod()-2); } modint operator-()const{ modint neg; neg.r=std::min(-r,remod()-r); return neg; } modint&operator/=(const modint&t){ return to_modint()*=t.inv(); } modint&operator*=(const modint&t){ r=UInt(UInt2(r)*t.r%mod()); return to_modint(); } modint&operator+=(const modint&t){ r+=t.r; r=std::min(r,r-remod()); return to_modint(); } modint&operator-=(const modint&t){ r-=t.r; r=std::min(r,r+remod()); return to_modint(); } modint operator+(const modint&t)const{return modint(to_modint())+=t;} modint operator-(const modint&t)const{return modint(to_modint())-=t;} modint operator*(const modint&t)const{return modint(to_modint())*=t;} modint operator/(const modint&t)const{return modint(to_modint())/=t;} auto operator==(const modint&t)const{return to_modint().getr()==t.getr();} auto operator!=(const modint&t)const{return to_modint().getr()!=t.getr();} auto operator<=(const modint&t)const{return to_modint().getr()<=t.getr();} auto operator>=(const modint&t)const{return to_modint().getr()>=t.getr();} auto operator<(const modint&t)const{return to_modint().getr()<t.getr();} auto operator>(const modint&t)const{return to_modint().getr()>t.getr();} Int rem()const{ UInt R=to_modint().getr(); return R-(R>(UInt)mod()/2)*mod(); } constexpr void setr(UInt rr){ r=rr; } constexpr UInt getr()const{ return r; } static uint64_t modmod8(){return uint64_t(8*modmod());} void add_unsafe(UInt t){r+=t;} void pseudonormalize(){r=std::min(r,r-modmod8());} modint const&normalize(){ if(r>=(UInt)mod()){ r%=mod(); } return to_modint(); } void setr_direct(UInt rr){r=rr;} UInt getr_direct()const{return r;} protected: UInt r; private: constexpr modint&to_modint(){return static_cast<modint&>(*this);} constexpr modint const&to_modint()const{return static_cast<modint const&>(*this);} }; template<typename modint> concept modint_type=std::is_base_of_v<modint_base<modint,typename modint::Int>,modint>; template<modint_type modint> decltype(std::cin)&operator>>(decltype(std::cin)&in,modint&x){ typename modint::UInt r; auto&res=in>>r; x.setr(r); return res; } template<modint_type modint> decltype(std::cout)&operator<<(decltype(std::cout)&out,modint const&x){ return out<<x.getr(); } template<auto m> struct modint:modint_base<modint<m>,decltype(m)>{ using Base=modint_base<modint<m>,decltype(m)>; using Base::Base; static constexpr Base::Int mod(){return m;} static constexpr Base::UInt remod(){return m;} auto getr()const{return Base::r;} }; template<typename Int=int> struct dynamic_modint:modint_base<dynamic_modint<Int>,Int>{ using Base=modint_base<dynamic_modint<Int>,Int>; using Base::Base; [[gnu::noinline,gnu::cold]]static Base::UInt m_reduce_reduced(Base::UInt2 ab){ if(mod()%2==0){ return typename Base::UInt(ab%mod()); } typename Base::UInt q= -(typename Base::UInt(ab)*inverse); auto high=typename Base::UInt(ab>>Base::bits); auto low=typename Base::UInt(typename Base::UInt2(q)*typename Base::UInt(mod())>>Base::bits); return high>=low?high-low:high-low+mod(); } static Base::UInt m_reduce(Base::UInt2 ab){ if(imod()==0)[[unlikely]]{ return m_reduce_reduced(ab); } typename Base::UInt2 m=typename Base::UInt(ab)*imod(); return typename Base::UInt((ab+m*mod())>>Base::bits); } static Base::UInt m_transform(Base::UInt a){ if(mod()%2==0)[[unlikely]]{ return a; }else{ return m_reduce(a*pw128()); } } dynamic_modint&operator*=(const dynamic_modint&t){ Base::r=m_reduce(typename Base::UInt2(Base::r)*t.r); return*this; } void setr(Base::UInt rr){ Base::r=m_transform(rr); } Base::UInt getr()const{ typename Base::UInt res=m_reduce(Base::r); return std::min(res,res-mod()); } static Int mod(){return m;} static Base::UInt remod(){return rm;} static Base::UInt imod(){return im;} static Base::UInt2 pw128(){return r2;} static void switch_mod(Int nm){ m=nm; bool lazy=m%2&&typename Base::UInt(m)<=typename Base::UInt(-1)/4; rm=typename Base::UInt(m)*(lazy?2:1); inverse=m%2?inv2(-m):0; im=lazy?inverse:0; r2=static_cast<Base::UInt>(static_cast<Base::UInt2>(-1)%m+1); } auto static with_mod(Int tmp,auto callback){ struct scoped{ Int prev=mod(); ~scoped(){switch_mod(prev);} }_; switch_mod(tmp); return callback(); } private: static inline thread_local Int m=1; static inline thread_local Base::UInt im= -1,r2=0,inverse= -1,rm=2; }; }
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