CP-Algorithms Library

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:heavy_check_mark: cp-algo/structures/bit_array.hpp

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#ifndef CP_ALGO_STRUCTURES_BIT_ARRAY_HPP
#define CP_ALGO_STRUCTURES_BIT_ARRAY_HPP
#include "../util/bit.hpp"
#include "../util/big_alloc.hpp"
#include <cassert>
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo::structures {
    template<typename C>
    concept Resizable = requires(C& c, std::size_t n) { c.resize(n); };

    template<class Cont>
    struct _bit_array {
        using word_t = typename Cont::value_type;
        static constexpr size_t width = bit_width<word_t>;
        size_t words, n;
        alignas(32) Cont data;

        constexpr void resize(size_t N) {
            n = N;
            words = (n + width - 1) / width;
            if constexpr (Resizable<Cont>) {
                data.resize(words);
            } else {
                assert(std::size(data) >= words);
            }
        }

        constexpr _bit_array(): data() {
            if constexpr (!Resizable<Cont>) {
                resize(std::size(data) * width);
            } else {
                resize(0);
            }
        }
        constexpr _bit_array(size_t N): data() {
            resize(N);
        }

        constexpr word_t& word(size_t x) {
            return data[x];
        }
        constexpr word_t word(size_t x) const {
            return data[x];
        }
        constexpr void set_all(word_t val = -1) {
            for(size_t i = 0; i < words; i++) {
                data[i] = val;
            }
        }
        constexpr void reset() {
            set_all(0);
        }
        constexpr void set(size_t x) {
            word(x / width) |= 1ULL << (x % width);
        }
        constexpr void reset(size_t x) {
            word(x / width) &= ~(1ULL << (x % width));
        }
        constexpr void flip(size_t x) {
            word(x / width) ^= 1ULL << (x % width);
        }
        constexpr bool test(size_t x) const {
            return (word(x / width) >> (x % width)) & 1;
        }
        constexpr bool operator[](size_t x) const {
            return test(x);
        }
        constexpr size_t size() const {
            return n;
        }
        
        auto operator <=> (_bit_array const& t) const = default;
        
        constexpr _bit_array& xor_hint(_bit_array const& t, size_t hint) {
            for(size_t i = hint / width; i < words; i++) {
                data[i] ^= t.data[i];
            }
            return *this;
        }
        constexpr _bit_array& operator ^= (_bit_array const& t) {
            return xor_hint(t, 0);
        }
        constexpr _bit_array operator ^ (_bit_array const& t) const {
            return _bit_array(*this) ^= t;
        }
    };

    template<size_t N>
    using bit_array = _bit_array<std::array<uint64_t, (N + 63) / 64>>;
    using dynamic_bit_array = _bit_array<big_vector<uint64_t>>;
}
#pragma GCC pop_options
#endif // CP_ALGO_STRUCTURES_BIT_ARRAY_HPP

#line 1 "cp-algo/structures/bit_array.hpp"


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


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


#include <experimental/simd>
#include <cstdint>
#include <cstddef>
#include <memory>

#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif

#define CP_ALGO_SIMD_PRAGMA_PUSH \
    _Pragma("GCC push_options") \
    CP_ALGO_SIMD_AVX2_TARGET

CP_ALGO_SIMD_PRAGMA_PUSH
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>;

    dx4 abs(dx4 a) {
        return dx4{
            std::abs(a[0]),
            std::abs(a[1]),
            std::abs(a[2]),
            std::abs(a[3])
        };
    }

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

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

    inline u64x4 low32(u64x4 x) {
        return x & uint32_t(-1);
    }
    inline auto swap_bytes(auto x) {
        return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
    }
    inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
        auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
        x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
#else
        auto x_ninv = u64x4(u32x8(low32(x)) * imod);
        x += x_ninv * uint64_t(mod);
#endif
        return swap_bytes(x);
    }

    inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
        return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
#else
        return montgomery_reduce(x * y, mod, imod);
#endif
    }
    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)));
    }
    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>
    inline bool is_aligned(const auto* p) noexcept {
        return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
    }

    template<class Target>
    inline Target& vector_cast(auto &&p) {
        return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
    }
}
#pragma GCC pop_options

#line 6 "cp-algo/util/bit.hpp"
#include <array>
#include <bit>

#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"avx2,bmi,bmi2,lzcnt,popcnt\")")
#else
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"bmi,bmi2,lzcnt,popcnt\")")
#endif

#define CP_ALGO_BIT_PRAGMA_PUSH \
    _Pragma("GCC push_options") \
    CP_ALGO_BIT_OPS_TARGET

CP_ALGO_BIT_PRAGMA_PUSH
namespace cp_algo {
    template<typename Uint>
    constexpr size_t bit_width = sizeof(Uint) * 8;

    // n < 64
    uint64_t mask(size_t n) {
        return (1ULL << n) - 1;
    }
    size_t order_of_bit(auto x, size_t k) {
        return k ? std::popcount(x << (bit_width<decltype(x)> - k)) : 0;
    }
    inline size_t kth_set_bit(uint64_t x, size_t k) {
        return std::countr_zero(_pdep_u64(1ULL << k, x));
    }
    template<int fl = 0>
    void with_bit_floor(size_t n, auto &&callback) {
        if constexpr (fl >= 63) {
            return;
        } else if (n >> (fl + 1)) {
            with_bit_floor<fl + 1>(n, callback);
        } else {
            callback.template operator()<1ULL << fl>();
        }
    }
    void with_bit_ceil(size_t n, auto &&callback) {
        with_bit_floor(n, [&]<size_t N>() {
            if(N == n) {
                callback.template operator()<N>();
            } else {
                callback.template operator()<N << 1>();
            }
        });
    }

    inline uint32_t read_bits(char const* p) {
        return _mm256_movemask_epi8(__m256i(vector_cast<u8x32 const>(p[0]) + (127 - '0')));
    }
    inline uint64_t read_bits64(char const* p) {
        return read_bits(p) | (uint64_t(read_bits(p + 32)) << 32);
    }

    inline void write_bits(char *p, uint32_t bits) {
        static constexpr u8x32 shuffler = {
            0, 0, 0, 0, 0, 0, 0, 0,
            1, 1, 1, 1, 1, 1, 1, 1,
            2, 2, 2, 2, 2, 2, 2, 2,
            3, 3, 3, 3, 3, 3, 3, 3
        };
        auto shuffled = u8x32(_mm256_shuffle_epi8(__m256i() + bits, __m256i(shuffler)));
        static constexpr u8x32 mask = {
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128
        };
        for(int z = 0; z < 32; z++) {
            p[z] = shuffled[z] & mask[z] ? '1' : '0';
        }
    }
    inline void write_bits64(char *p, uint64_t bits) {
        write_bits(p, uint32_t(bits));
        write_bits(p + 32, uint32_t(bits >> 32));
    }
}
#pragma GCC pop_options

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



#include <set>
#include <map>
#include <deque>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#line 12 "cp-algo/util/big_alloc.hpp"
#include <iostream>
#include <generator>
#include <forward_list>

// 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, 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;
        }
    };

    template<typename T> using big_vector = std::vector<T, big_alloc<T>>;
    template<typename T> using big_basic_string = std::basic_string<T, std::char_traits<T>, big_alloc<T>>;
    template<typename T> using big_deque = std::deque<T, big_alloc<T>>;
    template<typename T> using big_stack = std::stack<T, big_deque<T>>;
    template<typename T> using big_queue = std::queue<T, big_deque<T>>;
    template<typename T> using big_priority_queue = std::priority_queue<T, big_vector<T>>;
    template<typename T> using big_forward_list = std::forward_list<T, big_alloc<T>>;
    using big_string = big_basic_string<char>;

    template<typename Key, typename Value, typename Compare = std::less<Key>>
    using big_map = std::map<Key, Value, Compare, big_alloc<std::pair<const Key, Value>>>;
    template<typename T, typename Compare = std::less<T>>
    using big_multiset = std::multiset<T, Compare, big_alloc<T>>;
    template<typename T, typename Compare = std::less<T>>
    using big_set = std::set<T, Compare, big_alloc<T>>;
    template<typename Ref, typename V = void>

    using big_generator = std::generator<Ref, V, big_alloc<std::byte>>;
}

// Deduction guide to make elements_of with big_generator default to big_alloc
namespace std::ranges {
    template<typename Ref, typename V>
    elements_of(cp_algo::big_generator<Ref, V>&&) -> elements_of<cp_algo::big_generator<Ref, V>&&, cp_algo::big_alloc<std::byte>>;
}


#line 5 "cp-algo/structures/bit_array.hpp"
#include <cassert>
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo::structures {
    template<typename C>
    concept Resizable = requires(C& c, std::size_t n) { c.resize(n); };

    template<class Cont>
    struct _bit_array {
        using word_t = typename Cont::value_type;
        static constexpr size_t width = bit_width<word_t>;
        size_t words, n;
        alignas(32) Cont data;

        constexpr void resize(size_t N) {
            n = N;
            words = (n + width - 1) / width;
            if constexpr (Resizable<Cont>) {
                data.resize(words);
            } else {
                assert(std::size(data) >= words);
            }
        }

        constexpr _bit_array(): data() {
            if constexpr (!Resizable<Cont>) {
                resize(std::size(data) * width);
            } else {
                resize(0);
            }
        }
        constexpr _bit_array(size_t N): data() {
            resize(N);
        }

        constexpr word_t& word(size_t x) {
            return data[x];
        }
        constexpr word_t word(size_t x) const {
            return data[x];
        }
        constexpr void set_all(word_t val = -1) {
            for(size_t i = 0; i < words; i++) {
                data[i] = val;
            }
        }
        constexpr void reset() {
            set_all(0);
        }
        constexpr void set(size_t x) {
            word(x / width) |= 1ULL << (x % width);
        }
        constexpr void reset(size_t x) {
            word(x / width) &= ~(1ULL << (x % width));
        }
        constexpr void flip(size_t x) {
            word(x / width) ^= 1ULL << (x % width);
        }
        constexpr bool test(size_t x) const {
            return (word(x / width) >> (x % width)) & 1;
        }
        constexpr bool operator[](size_t x) const {
            return test(x);
        }
        constexpr size_t size() const {
            return n;
        }
        
        auto operator <=> (_bit_array const& t) const = default;
        
        constexpr _bit_array& xor_hint(_bit_array const& t, size_t hint) {
            for(size_t i = hint / width; i < words; i++) {
                data[i] ^= t.data[i];
            }
            return *this;
        }
        constexpr _bit_array& operator ^= (_bit_array const& t) {
            return xor_hint(t, 0);
        }
        constexpr _bit_array operator ^ (_bit_array const& t) const {
            return _bit_array(*this) ^= t;
        }
    };

    template<size_t N>
    using bit_array = _bit_array<std::array<uint64_t, (N + 63) / 64>>;
    using dynamic_bit_array = _bit_array<big_vector<uint64_t>>;
}
#pragma GCC pop_options


#ifndef CP_ALGO_STRUCTURES_BIT_ARRAY_HPP
#define CP_ALGO_STRUCTURES_BIT_ARRAY_HPP
#include "../util/bit.hpp"
#include "../util/big_alloc.hpp"
#include <cassert>
CP_ALGO_SIMD_PRAGMA_PUSHnamespace cp_algo::structures{template<typename C>concept Resizable=requires(C&c,std::size_t n){c.resize(n);};template<class Cont>struct _bit_array{using word_t=typename Cont::value_type;static constexpr size_t width=bit_width<word_t>;size_t words,n;alignas(32)Cont data;constexpr void resize(size_t N){n=N;words=(n+width-1)/width;if constexpr(Resizable<Cont>){data.resize(words);}else{assert(std::size(data)>=words);}}constexpr _bit_array():data(){if constexpr(!Resizable<Cont>){resize(std::size(data)*width);}else{resize(0);}}constexpr _bit_array(size_t N):data(){resize(N);}constexpr word_t&word(size_t x){return data[x];}constexpr word_t word(size_t x)const{return data[x];}constexpr void set_all(word_t val=-1){for(size_t i=0;i<words;i++){data[i]=val;}}constexpr void reset(){set_all(0);}constexpr void set(size_t x){word(x/width)|=1ULL<<(x%width);}constexpr void reset(size_t x){word(x/width)&=~(1ULL<<(x%width));}constexpr void flip(size_t x){word(x/width)^=1ULL<<(x%width);}constexpr bool test(size_t x)const{return(word(x/width)>>(x%width))&1;}constexpr bool operator[](size_t x)const{return test(x);}constexpr size_t size()const{return n;}auto operator<=>(_bit_array const&t)const=default;constexpr _bit_array&xor_hint(_bit_array const&t,size_t hint){for(size_t i=hint/width;i<words;i++){data[i]^=t.data[i];}return*this;}constexpr _bit_array&operator^=(_bit_array const&t){return xor_hint(t,0);}constexpr _bit_array operator^(_bit_array const&t)const{return _bit_array(*this)^=t;}};template<size_t N>using bit_array=_bit_array<std::array<uint64_t,(N+63)/64>>;using dynamic_bit_array=_bit_array<big_vector<uint64_t>>;}
#pragma GCC pop_options
#endif

#line 1 "cp-algo/structures/bit_array.hpp"
#line 1 "cp-algo/util/bit.hpp"
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#include <cstdint>
#include <cstddef>
#include <memory>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif
#define CP_ALGO_SIMD_PRAGMA_PUSH \
_Pragma("GCC push_options")\CP_ALGO_SIMD_AVX2_TARGETCP_ALGO_SIMD_PRAGMA_PUSHnamespace 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>;dx4 abs(dx4 a){return dx4{std::abs(a[0]),std::abs(a[1]),std::abs(a[2]),std::abs(a[3])};}static constexpr dx4 magic=dx4()+(3ULL<<51);inline i64x4 lround(dx4 x){return i64x4(x+magic)-i64x4(magic);}inline dx4 to_double(i64x4 x){return dx4(x+i64x4(magic))-magic;}inline dx4 round(dx4 a){return dx4{std::nearbyint(a[0]),std::nearbyint(a[1]),std::nearbyint(a[2]),std::nearbyint(a[3])};}inline u64x4 low32(u64x4 x){return x&uint32_t(-1);}inline auto swap_bytes(auto x){return decltype(x)(__builtin_shufflevector(u32x8(x),u32x8(x),1,0,3,2,5,4,7,6));}inline u64x4 montgomery_reduce(u64x4 x,uint32_t mod,uint32_t imod){
#ifdef __AVX2__
auto x_ninv=u64x4(_mm256_mul_epu32(__m256i(x),__m256i()+imod));x+=u64x4(_mm256_mul_epu32(__m256i(x_ninv),__m256i()+mod));
#else
auto x_ninv=u64x4(u32x8(low32(x))*imod);x+=x_ninv*uint64_t(mod);
#endif
return swap_bytes(x);}inline u64x4 montgomery_mul(u64x4 x,u64x4 y,uint32_t mod,uint32_t imod){
#ifdef __AVX2__
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x),__m256i(y))),mod,imod);
#else
return montgomery_reduce(x*y,mod,imod);
#endif
}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)));}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>inline bool is_aligned(const auto*p)noexcept{return(reinterpret_cast<std::uintptr_t>(p)%Align)==0;}template<class Target>inline Target&vector_cast(auto&&p){return*reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));}}
#pragma GCC pop_options
#line 6 "cp-algo/util/bit.hpp"
#include <array>
#include <bit>
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"avx2,bmi,bmi2,lzcnt,popcnt\")")
#else
#define CP_ALGO_BIT_OPS_TARGET _Pragma("GCC target(\"bmi,bmi2,lzcnt,popcnt\")")
#endif
#define CP_ALGO_BIT_PRAGMA_PUSH \
_Pragma("GCC push_options")\CP_ALGO_BIT_OPS_TARGETCP_ALGO_BIT_PRAGMA_PUSHnamespace cp_algo{template<typename Uint>constexpr size_t bit_width=sizeof(Uint)*8;uint64_t mask(size_t n){return(1ULL<<n)-1;}size_t order_of_bit(auto x,size_t k){return k?std::popcount(x<<(bit_width<decltype(x)>-k)):0;}inline size_t kth_set_bit(uint64_t x,size_t k){return std::countr_zero(_pdep_u64(1ULL<<k,x));}template<int fl=0>void with_bit_floor(size_t n,auto&&callback){if constexpr(fl>=63){return;}else if(n>>(fl+1)){with_bit_floor<fl+1>(n,callback);}else{callback.template operator()<1ULL<<fl>();}}void with_bit_ceil(size_t n,auto&&callback){with_bit_floor(n,[&]<size_t N>(){if(N==n){callback.template operator()<N>();}else{callback.template operator()<N<<1>();}});}inline uint32_t read_bits(char const*p){return _mm256_movemask_epi8(__m256i(vector_cast<u8x32 const>(p[0])+(127-'0')));}inline uint64_t read_bits64(char const*p){return read_bits(p)|(uint64_t(read_bits(p+32))<<32);}inline void write_bits(char*p,uint32_t bits){static constexpr u8x32 shuffler={0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3};auto shuffled=u8x32(_mm256_shuffle_epi8(__m256i()+bits,__m256i(shuffler)));static constexpr u8x32 mask={1,2,4,8,16,32,64,128,1,2,4,8,16,32,64,128,1,2,4,8,16,32,64,128,1,2,4,8,16,32,64,128};for(int z=0;z<32;z++){p[z]=shuffled[z]&mask[z]?'1':'0';}}inline void write_bits64(char*p,uint64_t bits){write_bits(p,uint32_t(bits));write_bits(p+32,uint32_t(bits>>32));}}
#pragma GCC pop_options
#line 1 "cp-algo/util/big_alloc.hpp"
#include <set>
#include <map>
#include <deque>
#include <stack>
#include <queue>
#include <vector>
#include <string>
#line 12 "cp-algo/util/big_alloc.hpp"
#include <iostream>
#include <generator>
#include <forward_list>
#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,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;}};template<typename T>using big_vector=std::vector<T,big_alloc<T>>;template<typename T>using big_basic_string=std::basic_string<T,std::char_traits<T>,big_alloc<T>>;template<typename T>using big_deque=std::deque<T,big_alloc<T>>;template<typename T>using big_stack=std::stack<T,big_deque<T>>;template<typename T>using big_queue=std::queue<T,big_deque<T>>;template<typename T>using big_priority_queue=std::priority_queue<T,big_vector<T>>;template<typename T>using big_forward_list=std::forward_list<T,big_alloc<T>>;using big_string=big_basic_string<char>;template<typename Key,typename Value,typename Compare=std::less<Key>>using big_map=std::map<Key,Value,Compare,big_alloc<std::pair<const Key,Value>>>;template<typename T,typename Compare=std::less<T>>using big_multiset=std::multiset<T,Compare,big_alloc<T>>;template<typename T,typename Compare=std::less<T>>using big_set=std::set<T,Compare,big_alloc<T>>;template<typename Ref,typename V=void>using big_generator=std::generator<Ref,V,big_alloc<std::byte>>;}namespace std::ranges{template<typename Ref,typename V>elements_of(cp_algo::big_generator<Ref,V>&&)->elements_of<cp_algo::big_generator<Ref,V>&&,cp_algo::big_alloc<std::byte>>;}
#line 5 "cp-algo/structures/bit_array.hpp"
#include <cassert>
CP_ALGO_SIMD_PRAGMA_PUSHnamespace cp_algo::structures{template<typename C>concept Resizable=requires(C&c,std::size_t n){c.resize(n);};template<class Cont>struct _bit_array{using word_t=typename Cont::value_type;static constexpr size_t width=bit_width<word_t>;size_t words,n;alignas(32)Cont data;constexpr void resize(size_t N){n=N;words=(n+width-1)/width;if constexpr(Resizable<Cont>){data.resize(words);}else{assert(std::size(data)>=words);}}constexpr _bit_array():data(){if constexpr(!Resizable<Cont>){resize(std::size(data)*width);}else{resize(0);}}constexpr _bit_array(size_t N):data(){resize(N);}constexpr word_t&word(size_t x){return data[x];}constexpr word_t word(size_t x)const{return data[x];}constexpr void set_all(word_t val=-1){for(size_t i=0;i<words;i++){data[i]=val;}}constexpr void reset(){set_all(0);}constexpr void set(size_t x){word(x/width)|=1ULL<<(x%width);}constexpr void reset(size_t x){word(x/width)&=~(1ULL<<(x%width));}constexpr void flip(size_t x){word(x/width)^=1ULL<<(x%width);}constexpr bool test(size_t x)const{return(word(x/width)>>(x%width))&1;}constexpr bool operator[](size_t x)const{return test(x);}constexpr size_t size()const{return n;}auto operator<=>(_bit_array const&t)const=default;constexpr _bit_array&xor_hint(_bit_array const&t,size_t hint){for(size_t i=hint/width;i<words;i++){data[i]^=t.data[i];}return*this;}constexpr _bit_array&operator^=(_bit_array const&t){return xor_hint(t,0);}constexpr _bit_array operator^(_bit_array const&t)const{return _bit_array(*this)^=t;}};template<size_t N>using bit_array=_bit_array<std::array<uint64_t,(N+63)/64>>;using dynamic_bit_array=_bit_array<big_vector<uint64_t>>;}
#pragma GCC pop_options
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