cp-library
競技プログラミング用 C++ ライブラリ
test/convolution_mod.test.cpp
test/convolution_mod.test.cpp · GitHub で見る
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コード
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"
#include "../convolution/convolution_mod.hpp"
#include "../components/fast_io_bulk.hpp"
#include <array>
#include <cstddef>
#include <cstdint>
#include <vector>
int main() {
FastInput input;
FastOutput output;
int n = 0, m = 0;
input.read(n);
input.read(m);
std::vector<std::uint32_t> a(n), b(m);
for (auto *values : {&a, &b}) {
std::size_t offset = 0;
read_unsigned_blocks(input, values->size(), [&](const std::uint32_t *block, std::size_t count) {
std::copy(block, block + count, values->data() + offset);
offset += count;
});
}
auto result = convolution_mod(a, b, 1000000007);
write_unsigned_records<1>(output, result.size(), [&](std::size_t i) {
return std::array<std::uint32_t, 1>{result[i]};
});
}
#line 1 "test/convolution_mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"
#line 1 "convolution/convolution_mod.hpp"
#line 1 "components/ntt_mod.hpp"
#include <algorithm>
#include <bit>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <vector>
#if defined(__x86_64__) || defined(__i386__)
#include <immintrin.h>
#endif
namespace ntt_mod_detail {
template <std::uint32_t mod> struct Vector;
template <std::uint32_t mod>
std::uint32_t power(std::uint32_t a, std::uint32_t k) {
std::uint32_t result = 1;
for (; k; k >>= 1, a = std::uint64_t(a) * a % mod)
if (k & 1) result = std::uint64_t(result) * a % mod;
return result;
}
template <std::uint32_t mod>
void butterfly(std::uint32_t *a, std::size_t n, std::size_t half,
const std::uint32_t *roots, const std::uint32_t *quotients) {
for (std::size_t start = 0; start < n; start += 2 * half)
for (std::size_t j = 0; j < half; ++j) {
std::uint32_t x = a[start + j], v = a[start + j + half];
std::uint32_t q = std::uint64_t(v) * quotients[j] >> 32;
std::uint32_t y = v * roots[j] - q * mod;
if (y >= mod) y -= mod;
a[start + j] = x + y < mod ? x + y : x + y - mod;
a[start + j + half] = x >= y ? x - y : x + mod - y;
}
}
#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void butterfly_avx2(std::uint32_t *a, std::size_t n, std::size_t half,
const std::uint32_t *roots, const std::uint32_t *quotients) {
using V = Vector<mod>;
for (std::size_t start = 0; start < n; start += 2 * half)
for (std::size_t j = 0; j < half; j += 8) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j));
auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + half));
auto r = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + j));
auto q = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + j));
y = V::multiply(y, r, q);
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j), V::add(x, y));
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + half), V::subtract(x, y));
}
}
#endif
template <std::uint32_t mod>
std::uint32_t shoup(std::uint32_t value, std::uint32_t factor, std::uint32_t quotient) {
std::uint32_t q = std::uint64_t(value) * quotient >> 32;
std::uint32_t result = value * factor - q * mod;
return result < mod ? result : result - mod;
}
template <std::uint32_t mod>
void forward_stage(std::uint32_t *a, std::size_t n, std::size_t half,
const std::uint32_t *roots, const std::uint32_t *quotients) {
for (std::size_t start = 0; start < n; start += 2 * half)
for (std::size_t j = 0; j < half; ++j) {
std::uint32_t x = a[start + j], y = a[start + j + half];
a[start + j] = x + y < mod ? x + y : x + y - mod;
std::uint32_t difference = x >= y ? x - y : x + mod - y;
a[start + j + half] = shoup<mod>(difference, roots[j], quotients[j]);
}
}
#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void forward_stage_avx2(std::uint32_t *a, std::size_t n, std::size_t half,
const std::uint32_t *roots, const std::uint32_t *quotients) {
using V = Vector<mod>;
for (std::size_t start = 0; start < n; start += 2 * half)
for (std::size_t j = 0; j < half; j += 8) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j));
auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + half));
auto r = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + j));
auto q = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + j));
auto difference = V::multiply(V::subtract(x, y), r, q);
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j), V::add(x, y));
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + half), difference);
}
}
#endif
#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
struct Vector {
static constexpr std::uint32_t range = mod < (std::uint32_t(1) << 30) ? 2 * mod : mod;
__attribute__((target("avx2"), always_inline))
static inline __m256i add(__m256i x, __m256i y) {
auto sum = _mm256_add_epi32(x, y);
return _mm256_min_epu32(sum, _mm256_sub_epi32(sum, _mm256_set1_epi32(range)));
}
__attribute__((target("avx2"), always_inline))
static inline __m256i subtract(__m256i x, __m256i y) {
auto difference = _mm256_sub_epi32(x, y);
return _mm256_min_epu32(difference, _mm256_add_epi32(difference, _mm256_set1_epi32(range)));
}
__attribute__((target("avx2"), always_inline))
static inline __m256i multiply(__m256i x, __m256i factor, __m256i quotient) {
auto even = _mm256_mul_epu32(x, quotient);
auto odd = _mm256_mul_epu32(_mm256_srli_epi64(x, 32), _mm256_srli_epi64(quotient, 32));
auto q = _mm256_blend_epi32(_mm256_srli_epi64(even, 32), odd, 0xaa);
auto result = _mm256_sub_epi32(_mm256_mullo_epi32(x, factor), _mm256_mullo_epi32(q, _mm256_set1_epi32(mod)));
if constexpr (range == 2 * mod) return result;
return _mm256_min_epu32(result, _mm256_sub_epi32(result, _mm256_set1_epi32(mod)));
}
};
template <std::uint32_t mod, bool inverse>
__attribute__((target("avx2")))
void leaf_avx2(std::uint32_t *a, std::size_t n, const std::uint32_t *roots, const std::uint32_t *quotients) {
using V = Vector<mod>;
auto r4 = _mm256_broadcastsi128_si256(_mm_loadu_si128(reinterpret_cast<const __m128i *>(roots + 4)));
auto q4 = _mm256_broadcastsi128_si256(_mm_loadu_si128(reinterpret_cast<const __m128i *>(quotients + 4)));
auto r2 = _mm256_setr_epi32(roots[2], roots[3], roots[2], roots[3], roots[2], roots[3], roots[2], roots[3]);
auto q2 = _mm256_setr_epi32(quotients[2], quotients[3], quotients[2], quotients[3], quotients[2], quotients[3], quotients[2], quotients[3]);
for (std::size_t i = 0; i < n; i += 8) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
if constexpr (!inverse) {
auto y = _mm256_permute2x128_si256(x, x, 1);
x = _mm256_blend_epi32(V::add(x, y), V::multiply(V::subtract(y, x), r4, q4), 0xf0);
y = _mm256_shuffle_epi32(x, 0x4e);
x = _mm256_blend_epi32(V::add(x, y), V::multiply(V::subtract(y, x), r2, q2), 0xcc);
y = _mm256_shuffle_epi32(x, 0xb1);
x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xaa);
} else {
auto y = _mm256_shuffle_epi32(x, 0xb1);
x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xaa);
x = _mm256_blend_epi32(x, V::multiply(x, r2, q2), 0xcc);
y = _mm256_shuffle_epi32(x, 0x4e);
x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xcc);
x = _mm256_blend_epi32(x, V::multiply(x, r4, q4), 0xf0);
y = _mm256_permute2x128_si256(x, x, 1);
x = _mm256_blend_epi32(V::add(x, y), V::subtract(y, x), 0xf0);
}
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), x);
}
}
template <std::uint32_t mod, bool inverse>
__attribute__((target("avx2")))
void pair_avx2(std::uint32_t *a, std::size_t n, std::size_t h, const std::uint32_t *roots, const std::uint32_t *quotients) {
using V = Vector<mod>;
for (std::size_t start = 0; start < n; start += 4 * h)
for (std::size_t j = 0; j < h; j += 8) {
auto x0 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j));
auto x1 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + h));
auto x2 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + 2 * h));
auto x3 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + start + j + 3 * h));
auto r0 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + 2 * h + j));
auto q0 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + 2 * h + j));
auto r1 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + 3 * h + j));
auto q1 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + 3 * h + j));
auto r2 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(roots + h + j));
auto q2 = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(quotients + h + j));
if constexpr (!inverse) {
auto y0 = V::add(x0, x2), y1 = V::add(x1, x3);
auto y2 = V::multiply(V::subtract(x0, x2), r0, q0);
auto y3 = V::multiply(V::subtract(x1, x3), r1, q1);
x0 = V::add(y0, y1); x1 = V::multiply(V::subtract(y0, y1), r2, q2);
x2 = V::add(y2, y3); x3 = V::multiply(V::subtract(y2, y3), r2, q2);
} else {
x1 = V::multiply(x1, r2, q2); x3 = V::multiply(x3, r2, q2);
auto y0 = V::add(x0, x1), y1 = V::subtract(x0, x1);
auto y2 = V::multiply(V::add(x2, x3), r0, q0);
auto y3 = V::multiply(V::subtract(x2, x3), r1, q1);
x0 = V::add(y0, y2); x2 = V::subtract(y0, y2);
x1 = V::add(y1, y3); x3 = V::subtract(y1, y3);
}
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j), x0);
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + h), x1);
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + 2 * h), x2);
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + start + j + 3 * h), x3);
}
}
#endif
#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void build_roots_avx2(std::uint32_t *roots, std::uint32_t *quotients, std::size_t half, std::uint32_t step) {
std::uint32_t initial[8], w = 1;
for (int i = 0; i < 8; ++i) {
initial[i] = w;
w = std::uint64_t(w) * step % mod;
}
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(initial));
auto factor = _mm256_set1_epi32(w), quotient = _mm256_set1_epi32((std::uint64_t(w) << 32) / mod);
for (std::size_t j = 0; j < half; j += 8) {
x = _mm256_min_epu32(x, _mm256_sub_epi32(x, _mm256_set1_epi32(mod)));
_mm256_storeu_si256(reinterpret_cast<__m256i *>(roots + j), x);
for (int k = 0; k < 8; ++k) quotients[j + k] = (std::uint64_t(roots[j + k]) << 32) / mod;
x = Vector<mod>::multiply(x, factor, quotient);
}
}
#endif
template <std::uint32_t mod, std::uint32_t root>
struct Plan {
std::vector<std::uint32_t> roots, quotients;
explicit Plan(std::size_t n, [[maybe_unused]] bool vectorized = false) : roots(n), quotients(n) {
static_assert(mod > 2 && mod < (std::uint32_t(1) << 31));
assert(std::has_single_bit(n) && (mod - 1) % n == 0);
if (n == 1) return;
std::size_t half = n / 2;
std::uint32_t step = power<mod>(root, (mod - 1) / n), w = 1;
#if defined(__x86_64__) || defined(__i386__)
if (vectorized && half >= 8) build_roots_avx2<mod>(roots.data() + half, quotients.data() + half, half, step);
else
#endif
for (std::size_t j = 0; j < half; ++j) {
roots[half + j] = w;
quotients[half + j] = (std::uint64_t(w) << 32) / mod;
w = std::uint64_t(w) * step % mod;
}
for (half /= 2; half; half /= 2)
for (std::size_t j = 0; j < half; ++j) {
roots[half + j] = roots[2 * half + 2 * j];
quotients[half + j] = quotients[2 * half + 2 * j];
}
}
};
template <std::uint32_t mod, std::uint32_t root>
void forward(std::vector<std::uint32_t> &a, const Plan<mod, root> &plan, [[maybe_unused]] bool vectorized) {
std::size_t half = a.size() / 2;
#if defined(__x86_64__) || defined(__i386__)
if (vectorized && a.size() >= 8) {
for (; half >= 16; half /= 4) pair_avx2<mod, false>(a.data(), a.size(), half / 2, plan.roots.data(), plan.quotients.data());
if (half == 8) forward_stage_avx2<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
leaf_avx2<mod, false>(a.data(), a.size(), plan.roots.data(), plan.quotients.data());
return;
}
#endif
for (; half; half /= 2) forward_stage<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
}
template <std::uint32_t mod, std::uint32_t root>
void backward(std::vector<std::uint32_t> &a, const Plan<mod, root> &plan, [[maybe_unused]] bool vectorized) {
std::size_t half = 1;
#if defined(__x86_64__) || defined(__i386__)
if (vectorized && a.size() >= 8) {
leaf_avx2<mod, true>(a.data(), a.size(), plan.roots.data(), plan.quotients.data());
half = 8;
for (; 2 * half < a.size(); half *= 4) pair_avx2<mod, true>(a.data(), a.size(), half, plan.roots.data(), plan.quotients.data());
if (half < a.size()) butterfly_avx2<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
return;
}
#endif
for (; half < a.size(); half *= 2) butterfly<mod>(a.data(), a.size(), half, plan.roots.data() + half, plan.quotients.data() + half);
}
#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void scale_avx2(std::uint32_t *a, std::size_t n, std::uint32_t factor, std::uint32_t quotient) {
auto r = _mm256_set1_epi32(factor), q = _mm256_set1_epi32(quotient);
for (std::size_t i = 0; i < n; i += 8) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
auto y = Vector<mod>::multiply(x, r, q);
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), _mm256_min_epu32(y, _mm256_sub_epi32(y, _mm256_set1_epi32(mod))));
}
}
#endif
template <std::uint32_t mod>
void scale(std::vector<std::uint32_t> &a, std::uint32_t factor, [[maybe_unused]] bool vectorized) {
std::uint32_t quotient = (std::uint64_t(factor) << 32) / mod;
#if defined(__x86_64__) || defined(__i386__)
if (vectorized && a.size() >= 8) {
scale_avx2<mod>(a.data(), a.size(), factor, quotient);
return;
}
#endif
for (auto &x : a) x = shoup<mod>(x, factor, quotient);
}
inline void bit_reverse(std::vector<std::uint32_t> &a) {
for (std::size_t i = 1, j = 0; i < a.size(); ++i) {
std::size_t bit = a.size() >> 1;
for (; j & bit; bit >>= 1) j ^= bit;
j ^= bit;
if (i < j) std::swap(a[i], a[j]);
}
}
template <std::uint32_t mod, std::uint32_t root>
void transform(std::vector<std::uint32_t> &a, bool inverse, bool vectorized) {
Plan<mod, root> plan(a.size(), vectorized);
if (inverse) {
bit_reverse(a);
backward(a, plan, vectorized);
std::reverse(a.begin() + 1, a.end());
scale<mod>(a, mod - (mod - 1) / a.size(), vectorized);
} else {
forward(a, plan, vectorized);
if constexpr (mod < (std::uint32_t(1) << 30)) for (auto &x : a) if (x >= mod) x -= mod;
bit_reverse(a);
}
}
template <std::uint32_t mod>
constexpr std::uint32_t negative_inverse = [] {
std::uint32_t value = mod;
for (int i = 0; i < 5; ++i) value *= 2 - mod * value;
return 0 - value;
}();
#if defined(__x86_64__) || defined(__i386__)
template <std::uint32_t mod>
__attribute__((target("avx2")))
void pointwise_avx2(std::uint32_t *a, const std::uint32_t *b, std::size_t n) {
auto p = _mm256_set1_epi32(mod), inverse = _mm256_set1_epi32(negative_inverse<mod>);
for (std::size_t i = 0; i < n; i += 8) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(b + i));
auto even = _mm256_mul_epu32(x, y);
auto odd = _mm256_mul_epu32(_mm256_srli_epi64(x, 32), _mm256_srli_epi64(y, 32));
auto qe = _mm256_mul_epu32(even, inverse), qo = _mm256_mul_epu32(odd, inverse);
even = _mm256_srli_epi64(_mm256_add_epi64(even, _mm256_mul_epu32(qe, p)), 32);
odd = _mm256_add_epi64(odd, _mm256_mul_epu32(qo, p));
x = _mm256_blend_epi32(even, odd, 0xaa);
x = _mm256_min_epu32(x, _mm256_sub_epi32(x, p));
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), x);
}
}
#endif
template <std::uint32_t mod>
void pointwise(std::vector<std::uint32_t> &a, const std::vector<std::uint32_t> &b, [[maybe_unused]] bool vectorized) {
#if defined(__x86_64__) || defined(__i386__)
if (vectorized && a.size() >= 8) {
pointwise_avx2<mod>(a.data(), b.data(), a.size());
return;
}
#endif
for (std::size_t i = 0; i < a.size(); ++i) {
std::uint64_t product = std::uint64_t(a[i]) * b[i];
std::uint32_t q = std::uint32_t(product) * negative_inverse<mod>;
std::uint32_t value = (product + std::uint64_t(q) * mod) >> 32;
a[i] = value < mod ? value : value - mod;
}
}
}
template <std::uint32_t mod, std::uint32_t root>
void ntt_mod(std::vector<std::uint32_t> &a, bool inverse = false) {
bool vectorized = false;
#if defined(__x86_64__) || defined(__i386__)
vectorized = __builtin_cpu_supports("avx2");
#endif
ntt_mod_detail::transform<mod, root>(a, inverse, vectorized);
}
#line 9 "convolution/convolution_mod.hpp"
#include <limits>
#include <utility>
#line 12 "convolution/convolution_mod.hpp"
namespace convolution_mod_detail {
using Word = std::uint32_t;
template <Word mod, Word root, class T>
std::vector<Word> multiply(const std::vector<T> &a, const std::vector<T> &b, Word factor = 1) {
const auto &small = a.size() <= b.size() ? a : b;
const auto &large = a.size() <= b.size() ? b : a;
std::size_t length = a.size() + b.size() - 1;
bool blocked = small.size() > 32 && large.size() / small.size() >= 8, square = &a == &b;
std::size_t n = std::bit_ceil(blocked ? 2 * small.size() - 1 : length), block = n - small.size() + 1;
std::vector<Word> x(n), y(square ? 0 : n);
auto reduce = [](T value) {
__int128_t r = __int128_t(value) % mod;
return Word(r < 0 ? r + mod : r);
};
for (std::size_t i = 0; i < small.size(); ++i) x[i] = reduce(small[i]);
if (small.size() <= 32) {
if (!square) for (std::size_t i = 0; i < large.size(); ++i) y[i] = reduce(large[i]);
const auto &other = square ? x : y;
std::vector<Word> result(length);
for (std::size_t i = 0; i < small.size(); ++i)
for (std::size_t j = 0; j < large.size(); ++j) result[i + j] = (result[i + j] + std::uint64_t(x[i]) * other[j]) % mod;
if (factor != 1) for (auto &v : result) v = std::uint64_t(v) * factor % mod;
return result;
}
bool vectorized = false;
#if defined(__x86_64__) || defined(__i386__)
vectorized = __builtin_cpu_supports("avx2");
#endif
ntt_mod_detail::Plan<mod, root> plan(n, vectorized);
ntt_mod_detail::forward(x, plan, vectorized);
Word scale = (std::uint64_t(1) << 32) % mod * (mod - (mod - 1) / n) % mod * factor % mod;
std::vector<Word> result(blocked ? length : 0);
auto &work = square ? x : y;
for (std::size_t start = 0; start < large.size(); start += block) {
std::size_t size = std::min(block, large.size() - start);
if (!square) {
for (std::size_t i = 0; i < size; ++i) y[i] = reduce(large[start + i]);
std::fill(y.begin() + size, y.end(), 0);
ntt_mod_detail::forward(y, plan, vectorized);
}
ntt_mod_detail::pointwise<mod>(work, x, vectorized);
ntt_mod_detail::backward(work, plan, vectorized);
std::reverse(work.begin() + 1, work.end());
ntt_mod_detail::scale<mod>(work, scale, vectorized);
if (!blocked) {
work.resize(length);
return std::move(work);
}
for (std::size_t i = 0; i < size + small.size() - 1; ++i) {
Word sum = result[start + i] + work[i];
result[start + i] = sum < mod ? sum : sum - mod;
}
}
return result;
}
inline constexpr Word p = 754974721, q = 1224736769, r = 2013265921;
inline constexpr __uint128_t modulus = __uint128_t(p) * q * r;
struct Reconstruction { std::uint64_t low; Word high; };
template <Word P = p, Word Q = q, Word R = r>
inline Reconstruction reconstruct(Word a, Word b, Word c) {
static const Word inverse_p = ntt_mod_detail::power<Q>(P, Q - 2);
static const Word inverse_pq = ntt_mod_detail::power<R>(std::uint64_t(P) * Q % R, R - 2);
std::uint64_t x = std::uint64_t(b + Q - a) * inverse_p % Q;
std::uint64_t low = a + std::uint64_t(P) * x;
std::uint64_t y = std::uint64_t(c + R - low % R) * inverse_pq % R;
return {low, Word(y)};
}
inline __uint128_t restore(Word a, Word b, Word c) {
auto [low, high] = reconstruct(a, b, c);
return low + __uint128_t(p) * q * high;
}
#if defined(__x86_64__) || defined(__i386__)
template <Word P, Word Q, Word R>
__attribute__((target("avx2")))
void combine(Word *a, const Word *b, const Word *c, std::size_t n) {
static_assert(P > 256 && Q > 256 && R > 256 && P + std::uint64_t(Q) + R < (std::uint64_t(1) << 32));
constexpr Word mod = 1000000007;
constexpr auto form = [](std::uint64_t x) { return Word(x % mod * ((std::uint64_t(1) << 32) % mod) % mod); };
constexpr Word place[3] = {form(std::uint64_t(Q) * R), form(std::uint64_t(P) * R), form(std::uint64_t(P) * Q)};
constexpr Word wrap = form(mod - std::uint64_t(P) * Q % mod * R % mod);
const auto p = _mm256_set1_epi32(mod), inverse = _mm256_set1_epi32(ntt_mod_detail::negative_inverse<mod>);
std::size_t i = 0;
for (; n - i >= 8; i += 8) {
auto x = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(a + i));
auto y = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(b + i));
auto z = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(c + i));
auto quotient = [&](__m256i a, __m256i b, __m256i c) __attribute__((target("avx2"), always_inline)) {
auto s = _mm256_mul_epu32(a, _mm256_set1_epi32((std::uint64_t(1) << 40) / P + 1));
s = _mm256_add_epi64(s, _mm256_mul_epu32(b, _mm256_set1_epi32((std::uint64_t(1) << 40) / Q + 1)));
s = _mm256_add_epi64(s, _mm256_mul_epu32(c, _mm256_set1_epi32((std::uint64_t(1) << 40) / R + 1)));
return _mm256_srli_epi64(_mm256_add_epi64(s, _mm256_set1_epi64x(std::uint64_t(1) << 39)), 40);
};
auto reduce = [&](__m256i a, __m256i b, __m256i c, __m256i t) __attribute__((target("avx2"), always_inline)) {
auto s = _mm256_add_epi64(_mm256_mul_epu32(a, _mm256_set1_epi32(place[0])), _mm256_mul_epu32(b, _mm256_set1_epi32(place[1])));
s = _mm256_add_epi64(s, _mm256_mul_epu32(c, _mm256_set1_epi32(place[2])));
s = _mm256_add_epi64(s, _mm256_mul_epu32(t, _mm256_set1_epi32(wrap)));
return _mm256_add_epi64(s, _mm256_mul_epu32(_mm256_mul_epu32(s, inverse), p));
};
auto xo = _mm256_srli_epi64(x, 32), yo = _mm256_srli_epi64(y, 32), zo = _mm256_srli_epi64(z, 32);
auto even = reduce(x, y, z, quotient(x, y, z)), odd = reduce(xo, yo, zo, quotient(xo, yo, zo));
x = _mm256_blend_epi32(_mm256_srli_epi64(even, 32), odd, 0xaa);
x = _mm256_min_epu32(x, _mm256_sub_epi32(x, p));
_mm256_storeu_si256(reinterpret_cast<__m256i *>(a + i), x);
}
for (; i < n; ++i) {
std::uint64_t t = (std::uint64_t(a[i]) * ((std::uint64_t(1) << 40) / P + 1) + std::uint64_t(b[i]) * ((std::uint64_t(1) << 40) / Q + 1) + std::uint64_t(c[i]) * ((std::uint64_t(1) << 40) / R + 1) + (std::uint64_t(1) << 39)) >> 40;
std::uint64_t sum = std::uint64_t(a[i]) * place[0] + std::uint64_t(b[i]) * place[1] + std::uint64_t(c[i]) * place[2] + std::uint64_t(t) * wrap;
auto q = Word(sum) * ntt_mod_detail::negative_inverse<mod>;
Word value = (sum + std::uint64_t(q) * mod) >> 32;
a[i] = value < mod ? value : value - mod;
}
}
#endif
template <Word P, Word PR, Word Q, Word QR, Word R, Word RR>
std::vector<Word> modular(const std::vector<Word> &a, const std::vector<Word> &b, Word mod) {
#if defined(__x86_64__) || defined(__i386__)
if constexpr (P + std::uint64_t(Q) + R < (std::uint64_t(1) << 32)) {
if (mod == 1000000007 && __uint128_t(std::min(a.size(), b.size())) * (mod - 1) * (mod - 1) * 4 < __uint128_t(P) * Q * R && __builtin_cpu_supports("avx2")) {
auto x = multiply<P, PR>(a, b, ntt_mod_detail::power<P>(std::uint64_t(Q) * R % P, P - 2));
auto y = multiply<Q, QR>(a, b, ntt_mod_detail::power<Q>(std::uint64_t(P) * R % Q, Q - 2));
auto z = multiply<R, RR>(a, b, ntt_mod_detail::power<R>(std::uint64_t(P) * Q % R, R - 2));
combine<P, Q, R>(x.data(), y.data(), z.data(), x.size());
return x;
}
}
#endif
auto x = multiply<P, PR>(a, b);
auto y = multiply<Q, QR>(a, b);
auto z = multiply<R, RR>(a, b);
std::uint64_t pq_mod = std::uint64_t(P) * Q % mod;
for (std::size_t i = 0; i < x.size(); ++i) {
auto [low, high] = reconstruct<P, Q, R>(x[i], y[i], z[i]);
x[i] = (low % mod + pq_mod * high) % mod;
}
return x;
}
}
template <class T>
std::vector<T> convolution_integer(const std::vector<T> &a, const std::vector<T> &b) {
static_assert(std::numeric_limits<T>::is_integer && sizeof(T) <= 8);
if (a.empty() || b.empty()) return {};
assert(a.size() + b.size() - 1 <= std::size_t(1) << 24);
auto x = convolution_mod_detail::multiply<convolution_mod_detail::p, 11>(a, b);
auto y = convolution_mod_detail::multiply<convolution_mod_detail::q, 3>(a, b);
auto z = convolution_mod_detail::multiply<convolution_mod_detail::r, 31>(a, b);
std::vector<T> result(x.size());
for (std::size_t i = 0; i < x.size(); ++i) {
auto value = convolution_mod_detail::restore(x[i], y[i], z[i]);
if constexpr (std::numeric_limits<T>::is_signed) {
__int128_t v = value > convolution_mod_detail::modulus / 2 ? __int128_t(value) - __int128_t(convolution_mod_detail::modulus) : __int128_t(value);
assert(std::numeric_limits<T>::lowest() <= v && v <= std::numeric_limits<T>::max());
result[i] = T(v);
} else {
assert(value <= std::numeric_limits<T>::max());
result[i] = T(value);
}
}
return result;
}
template <class T>
std::vector<std::uint32_t> convolution_mod(const std::vector<T> &a, const std::vector<T> &b, std::uint32_t mod) {
static_assert(std::numeric_limits<T>::is_integer && sizeof(T) <= 8);
assert(mod > 0);
if (a.empty() || b.empty()) return {};
assert(a.size() + b.size() - 1 <= std::size_t(1) << 24);
if (mod == 1) return std::vector<std::uint32_t>(a.size() + b.size() - 1);
std::vector<std::uint32_t> x(a.size()), y(&a == &b ? 0 : b.size());
auto reduce = [=](T value) {
__int128_t r = __int128_t(value) % mod;
return std::uint32_t(r < 0 ? r + mod : r);
};
std::transform(a.begin(), a.end(), x.begin(), reduce);
if (&a != &b) std::transform(b.begin(), b.end(), y.begin(), reduce);
const auto &other = &a == &b ? x : y;
if (std::min(x.size(), other.size()) <= 32) {
std::vector<std::uint32_t> result(x.size() + other.size() - 1);
for (std::size_t i = 0; i < x.size(); ++i)
for (std::size_t j = 0; j < other.size(); ++j) result[i + j] = (result[i + j] + std::uint64_t(x[i]) * other[j]) % mod;
return result;
}
if (mod == 998244353 && x.size() + other.size() - 1 <= std::size_t(1) << 23) return convolution_mod_detail::multiply<998244353, 3>(x, other);
constexpr std::uint32_t P = 167772161, Q = 469762049, R = 754974721;
if (__uint128_t(std::min(x.size(), other.size())) * (mod - 1) * (mod - 1) < __uint128_t(P) * Q * R)
return convolution_mod_detail::modular<P, 3, Q, 3, R, 11>(x, other, mod);
return convolution_mod_detail::modular<convolution_mod_detail::p, 11, convolution_mod_detail::q, 3, convolution_mod_detail::r, 31>(x, other, mod);
}
#line 1 "components/fast_io_bulk.hpp"
#line 1 "components/fast_io_output.hpp"
#line 1 "components/fast_io.hpp"
#line 5 "components/fast_io.hpp"
#include <array>
#line 8 "components/fast_io.hpp"
#include <charconv>
#line 11 "components/fast_io.hpp"
#include <cstdio>
#include <cstring>
#include <memory>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>
#if defined(__unix__) || defined(__APPLE__)
#include <sys/mman.h>
#include <sys/stat.h>
#include <unistd.h>
#endif
namespace fast_io_detail { struct BulkInput; struct BulkOutput; }
class FastInput {
friend struct fast_io_detail::BulkInput;
static constexpr std::size_t capacity = 1 << 16;
FILE *file = nullptr;
std::unique_ptr<char[]> buffer;
const char *current = "", *end = current;
std::string scratch;
void *mapping = nullptr;
std::size_t mapped_size = 0;
bool refill() {
if (!file) return false;
std::size_t n = std::fread(buffer.get(), 1, capacity, file);
current = buffer.get();
end = current + n;
return n;
}
static const char *scan(const char *p, const char *end) {
while (end - p >= 8) {
std::uint64_t x;
std::memcpy(&x, p, 8);
if ((x - 0x2121212121212121ULL) & ~x & 0x8080808080808080ULL) break;
p += 8;
}
while (p != end && static_cast<unsigned char>(*p) > ' ') ++p;
return p;
}
public:
explicit FastInput(FILE *input = stdin) {
#if defined(__unix__) || defined(__APPLE__)
struct stat status;
int fd = fileno(input);
auto offset = ftello(input);
if (fd >= 0 && offset >= 0 && !fstat(fd, &status) && S_ISREG(status.st_mode) && status.st_size > offset) {
mapped_size = status.st_size;
mapping = mmap(nullptr, mapped_size, PROT_READ, MAP_PRIVATE, fd, 0);
if (mapping != MAP_FAILED) {
current = static_cast<const char *>(mapping) + offset;
end = static_cast<const char *>(mapping) + mapped_size;
return;
}
mapping = nullptr;
}
#endif
file = input;
buffer = std::make_unique_for_overwrite<char[]>(capacity);
}
explicit FastInput(std::string_view input) : current(input.empty() ? "" : input.data()), end(current + input.size()) {}
FastInput(const FastInput &) = delete;
FastInput &operator=(const FastInput &) = delete;
~FastInput() {
#if defined(__unix__) || defined(__APPLE__)
if (mapping) munmap(mapping, mapped_size);
#endif
}
std::string_view token() {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return {};
}
const char *begin = current;
current = scan(current, end);
if (current != end || !file) return {begin, std::size_t(current - begin)};
scratch.assign(begin, end);
while (refill()) {
current = scan(current, end);
scratch.append(buffer.get(), std::size_t(current - buffer.get()));
if (current != end) break;
}
return scratch;
}
template <class T>
bool read(T &value) {
if constexpr (std::is_integral_v<T> && !std::is_same_v<T, bool>) {
while (true) {
while (current != end && static_cast<unsigned char>(*current) <= ' ') ++current;
if (current != end) break;
if (!refill()) return false;
}
if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4 && std::endian::native == std::endian::little) {
if (end - current >= 11) {
std::uint64_t x;
std::memcpy(&x, current, 8);
if (!(((x + 0x4646464646464646ULL) | (x - 0x3030303030303030ULL)) & 0x8080808080808080ULL)) {
x &= 0x0f0f0f0f0f0f0f0fULL;
x = (x * 10 + (x >> 8)) & 0x00ff00ff00ff00ffULL;
x = (x * 100 + (x >> 16)) & 0x0000ffff0000ffffULL;
std::uint64_t v = std::uint32_t(x * 10000 + (x >> 32));
int n = 8;
for (; n < 10 && static_cast<unsigned char>(current[n]) - unsigned('0') < 10; ++n)
v = v * 10 + (current[n] - '0');
if (static_cast<unsigned char>(current[n]) <= ' ' && v <= 0xffffffffULL) {
current += n;
value = T(v);
return true;
}
}
}
}
T parsed{};
auto result = std::from_chars(current, end, parsed);
if (result.ec == std::errc{} && (result.ptr != end ? static_cast<unsigned char>(*result.ptr) <= ' ' : !file)) {
current = result.ptr;
value = parsed;
return true;
}
}
auto s = token();
if (s.empty()) return false;
if constexpr (std::is_same_v<T, bool>) {
assert(s == "0" || s == "1");
value = s[0] == '1';
} else if constexpr (std::is_integral_v<T>) {
auto result = std::from_chars(s.data(), s.data() + s.size(), value);
assert(result.ec == std::errc{} && result.ptr == s.data() + s.size());
(void)result;
} else value = T(s);
return true;
}
};
class FastOutput {
friend struct fast_io_detail::BulkOutput;
inline static constexpr auto quads = [] {
std::array<std::array<char, 4>, 10000> table{};
for (int i = 0; i < 10000; ++i)
table[i] = {char('0' + i / 1000), char('0' + i / 100 % 10), char('0' + i / 10 % 10), char('0' + i % 10)};
return table;
}();
FILE *file;
std::unique_ptr<char[]> buffer = std::make_unique_for_overwrite<char[]>(1 << 16);
std::size_t capacity = 1 << 16, length = 0;
char *reserve(std::size_t n) {
if (n > capacity - length) {
if (!flush()) throw std::runtime_error("output failed");
if (n > capacity) {
std::size_t next = std::max(n, 2 * capacity);
buffer = std::make_unique_for_overwrite<char[]>(next);
capacity = next;
}
}
return buffer.get() + length;
}
public:
explicit FastOutput(FILE *output = stdout) : file(output) {}
FastOutput(const FastOutput &) = delete;
FastOutput &operator=(const FastOutput &) = delete;
~FastOutput() { flush(); }
bool flush() {
std::size_t offset = 0;
while (offset < length) {
auto n = std::fwrite(buffer.get() + offset, 1, length - offset, file);
if (!n) {
std::memmove(buffer.get(), buffer.get() + offset, length - offset);
length -= offset;
return false;
}
offset += n;
}
length = 0;
return std::fflush(file) == 0;
}
void write(char c) { *reserve(1) = c; ++length; }
void write(__uint128_t value) {
char digits[40];
char *end = digits + sizeof(digits), *begin = end;
do { *--begin = char('0' + value % 10); value /= 10; } while (value);
write(std::string_view(begin, end - begin));
}
void write(__int128_t value) {
__uint128_t magnitude = __uint128_t(value);
if (value < 0) write('-'), magnitude = 0 - magnitude;
write(magnitude);
}
void write(std::string_view s) {
char *out = reserve(s.size());
if (!s.empty()) std::memcpy(out, s.data(), s.size());
length += s.size();
}
template <class T> requires std::is_integral_v<T>
void write(T value) {
char *out = reserve(32);
if constexpr (std::is_same_v<T, bool>) *out = '0' + value, ++length;
else if constexpr (std::is_unsigned_v<T> && sizeof(T) == 4) {
char *p = out;
if (value >= 100000000) {
auto high = value / 100000000, low = value % 100000000;
p = std::to_chars(p, p + 2, high).ptr;
std::memcpy(p, quads[low / 10000].data(), 4);
std::memcpy(p + 4, quads[low % 10000].data(), 4);
p += 8;
} else if (value >= 10000) {
p = std::to_chars(p, p + 4, value / 10000).ptr;
std::memcpy(p, quads[value % 10000].data(), 4);
p += 4;
} else p = std::to_chars(p, p + 4, value).ptr;
length += p - out;
} else length += std::to_chars(out, out + 32, value).ptr - out;
}
template <class T> requires requires(const T &value, char *out) { value.decimal_capacity(); value.to_chars(out); }
void write(const T &value) {
char *out = reserve(value.decimal_capacity());
length += value.to_chars(out) - out;
}
template <class T>
void println(const T &value) { write(value); write('\n'); }
};
#line 7 "components/fast_io_output.hpp"
namespace fast_io_detail {
struct BulkOutput {
static char *small(char *out, std::uint32_t value) {
unsigned n = 1 + (value >= 10) + (value >= 100) + (value >= 1000);
if constexpr (std::endian::native == std::endian::little) {
std::uint32_t word;
std::memcpy(&word, FastOutput::quads[value].data(), 4);
word >>= (4 - n) * 8;
std::memcpy(out, &word, 4);
} else std::memcpy(out, FastOutput::quads[value].data() + 4 - n, n);
return out + n;
}
static char *number(char *out, std::uint32_t value) {
if (value >= 100000000) {
out = small(out, value / 100000000);
value %= 100000000;
std::memcpy(out, FastOutput::quads[value / 10000].data(), 4);
std::memcpy(out + 4, FastOutput::quads[value % 10000].data(), 4);
return out + 8;
}
if (value >= 10000) {
out = small(out, value / 10000);
std::memcpy(out, FastOutput::quads[value % 10000].data(), 4);
return out + 4;
}
return small(out, value);
}
template<std::size_t Fields, class Read>
#if defined(__GNUC__) || defined(__clang__)
[[gnu::noinline]]
#endif
static void records(FastOutput &out, std::size_t count, Read read) {
constexpr auto bytes = 11 * Fields;
constexpr auto block = std::max<std::size_t>(1, (1 << 16) / bytes);
for (std::size_t base = 0; base < count;) {
const auto n = std::min(count - base, block);
char *begin = out.reserve(n * bytes), *p = begin;
for (std::size_t i = 0; i < n; ++i) {
auto values = read(base + i);
for (std::size_t j = 0; j < Fields; ++j) {
p = number(p, std::uint32_t(values[j]));
*p++ = j + 1 == Fields ? '\n' : ' ';
}
}
out.length += p - begin;
base += n;
}
}
static void write(FastOutput &out, std::string_view text) {
if (text.size() <= (1 << 16)) return out.write(text);
if (out.length && !out.flush()) throw std::runtime_error("output failed");
std::size_t done = 0;
while (done < text.size()) {
const auto written = std::fwrite(text.data() + done, 1, text.size() - done, out.file);
if (!written) throw std::runtime_error("output failed");
done += written;
}
}
};
}
template<std::size_t Fields, class Read>
void write_unsigned_records(FastOutput &output, std::size_t count, Read read) {
static_assert(Fields > 0 && Fields <= std::numeric_limits<std::size_t>::max() / 11);
fast_io_detail::BulkOutput::records<Fields>(output, count, std::move(read));
}
#line 6 "components/fast_io_bulk.hpp"
#include <span>
#line 8 "components/fast_io_bulk.hpp"
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
#include <immintrin.h>
#pragma GCC push_options
_Pragma("GCC target(\"avx2\")")
#pragma GCC optimize("O3")
namespace fast_io_detail {
struct BulkInput {
alignas(32) static inline constexpr auto rows = [] {
std::array<std::array<unsigned char, 16>, 11> r{};
for (int n = 0; n <= 10; ++n)
for (int i = 0; i < 16; ++i) r[n][i] = i < 16 - n ? 128 : i - (16 - n);
return r;
}();
static constexpr std::size_t kChunk = 1 << 17, kCapacity = kChunk / 4 + 66;
static unsigned separators(__m256i bytes) {
return unsigned(_mm256_movemask_epi8(_mm256_cmpeq_epi8(_mm256_max_epu8(bytes, _mm256_set1_epi8(' ')), _mm256_set1_epi8(' '))));
}
[[gnu::always_inline]] static __m256i two(const char *&p, __m256i &invalid) {
const auto bytes = _mm256_loadu_si256(reinterpret_cast<const __m256i *>(p));
const unsigned sep = separators(bytes), a = std::countr_zero(sep), b = std::countr_zero(sep & (sep - 1));
if (a < 1 || a > 10 || b <= a + 1 || b - a - 1 > 10) [[unlikely]] {
invalid = _mm256_set1_epi32(-1);
p += std::min(b + 1, 32u);
return _mm256_setzero_si256();
}
const auto window = _mm256_inserti128_si256(bytes, _mm_loadu_si128(reinterpret_cast<const __m128i *>(p + a + 1)), 1);
const auto control = _mm256_set_m128i(_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[b - a - 1].data())),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[a].data())));
const auto digits = _mm256_shuffle_epi8(_mm256_sub_epi8(window, _mm256_set1_epi8('0')), control);
invalid = _mm256_or_si256(invalid, _mm256_subs_epu8(digits, _mm256_set1_epi8(9)));
p += b + 1;
return _mm256_madd_epi16(_mm256_maddubs_epi16(digits, _mm256_set1_epi16(0x010a)), _mm256_set1_epi32(0x00010064));
}
static std::uint32_t one(const char *&p, bool &bad) {
const auto bytes = _mm_loadu_si128(reinterpret_cast<const __m128i *>(p));
const auto spaces = _mm_cmpeq_epi8(_mm_max_epu8(bytes, _mm_set1_epi8(' ')), _mm_set1_epi8(' '));
const unsigned n = std::countr_zero(unsigned(_mm_movemask_epi8(spaces)) | 0x10000u);
if (n < 1 || n > 10) [[unlikely]] {
bad = true;
p += std::min(n + 1, 16u);
return 0;
}
const auto digits = _mm_shuffle_epi8(_mm_sub_epi8(bytes, _mm_set1_epi8('0')),
_mm_loadu_si128(reinterpret_cast<const __m128i *>(rows[n].data())));
const auto invalid = _mm_subs_epu8(digits, _mm_set1_epi8(9));
bad |= !_mm_testz_si128(invalid, invalid);
const auto groups = _mm_madd_epi16(_mm_maddubs_epi16(digits, _mm_set1_epi16(0x010a)), _mm_set1_epi32(0x00010064));
const auto halves = _mm_madd_epi16(_mm_packus_epi32(groups, groups), _mm_set1_epi32(0x00012710));
const std::uint64_t value = std::uint64_t(unsigned(_mm_cvtsi128_si32(halves))) * 100000000 + unsigned(_mm_extract_epi32(halves, 1));
bad |= value > 0xffffffffULL;
p += n + 1;
return std::uint32_t(value);
}
static const char *after_separator(const char *p) {
const unsigned mask = separators(_mm256_loadu_si256(reinterpret_cast<const __m256i *>(p)));
return mask ? p + std::countr_zero(mask) + 1 : nullptr;
}
static std::size_t lockstep(const char *(&streams)[4], const char *const (&end)[4], unsigned *const (&out)[4], __m256i &invalid) {
const char *p[4] = {streams[0], streams[1], streams[2], streams[3]};
std::size_t done = 0;
for (;;) {
std::ptrdiff_t left = end[0] - p[0];
for (int k = 1; k < 4; ++k) left = std::min(left, end[k] - p[k]);
const auto steps = std::min(left / 33, std::ptrdiff_t((kCapacity - done) / 2));
if (steps <= 0) break;
for (auto j = steps; j; --j, done += 2) {
const auto g0 = two(p[0], invalid), g1 = two(p[1], invalid), g2 = two(p[2], invalid), g3 = two(p[3], invalid);
const auto k = _mm256_set1_epi32(0x00012710);
const auto h01 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g0, g1), k));
const auto h23 = _mm256_castsi256_ps(_mm256_madd_epi16(_mm256_packus_epi32(g2, g3), k));
const auto high = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0x88));
const auto low = _mm256_castps_si256(_mm256_shuffle_ps(h01, h23, 0xdd));
const auto overflow = _mm256_or_si256(_mm256_cmpgt_epi32(high, _mm256_set1_epi32(42)),
_mm256_and_si256(_mm256_cmpeq_epi32(high, _mm256_set1_epi32(42)), _mm256_cmpgt_epi32(low, _mm256_set1_epi32(94967295))));
invalid = _mm256_or_si256(invalid, overflow);
const auto value = _mm256_add_epi32(_mm256_mullo_epi32(high, _mm256_set1_epi32(100000000)), low);
const auto q = _mm256_permutevar8x32_epi32(value, _mm256_setr_epi32(0, 4, 1, 5, 2, 6, 3, 7));
const auto q01 = _mm256_castsi256_si128(q), q23 = _mm256_extracti128_si256(q, 1);
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[0] + done), q01);
_mm_storeh_pd(reinterpret_cast<double *>(out[1] + done), _mm_castsi128_pd(q01));
_mm_storel_epi64(reinterpret_cast<__m128i *>(out[2] + done), q23);
_mm_storeh_pd(reinterpret_cast<double *>(out[3] + done), _mm_castsi128_pd(q23));
}
}
for (int k = 0; k < 4; ++k) streams[k] = p[k];
return done;
}
template <class Emit>
static std::size_t chunk_blocks(const char *&p, const char *limit, std::size_t count, unsigned *const (&out)[4], Emit &&emit) {
const auto bytes = std::min({kChunk, 2 * (count - 32), std::size_t(limit - p) - 64}) & ~std::size_t(3);
const std::size_t stream = bytes / 4;
const char *p1 = after_separator(p + stream), *p2 = after_separator(p + 2 * stream);
const char *p3 = after_separator(p + 3 * stream), *last = after_separator(p + bytes);
if (!p1 || !p2 || !p3 || !last) return 0;
const char *s[4] = {p, p1, p2, p3}, *const end[4] = {p1, p2, p3, last};
auto invalid = _mm256_setzero_si256();
const auto done = lockstep(s, end, out, invalid);
bool bad = !_mm256_testz_si256(invalid, invalid);
std::size_t n[4];
for (int k = 0; k < 4; ++k) {
n[k] = done;
while (s[k] < end[k] && n[k] < kCapacity) out[k][n[k]++] = one(s[k], bad);
bad |= s[k] != end[k];
}
const auto parsed = n[0] + n[1] + n[2] + n[3];
if (bad || parsed > count) return 0;
for (int k = 0; k < 4; ++k) emit(out[k], n[k]);
p = last;
return parsed;
}
static std::size_t chunk(const char *&p, const char *limit, unsigned *dst, std::size_t count, unsigned *scratch) {
unsigned *const out[4] = {dst, scratch, scratch + kCapacity, scratch + 2 * kCapacity};
bool first = true;
unsigned *next = dst;
return chunk_blocks(p, limit, count, out, [&](const unsigned *values, std::size_t n) {
if (!first) std::memcpy(next, values, n * sizeof(unsigned));
first = false;
next += n;
});
}
template <class Emit>
static void read_blocks(FastInput &in, std::size_t count, Emit emit) {
std::unique_ptr<unsigned[]> scratch;
std::size_t done = 0;
bool chunks = true;
while (done < count) {
const char *p = in.current;
while (p != in.end && static_cast<unsigned char>(*p) <= ' ') ++p;
while (chunks && count - done >= 1024 && in.end - p >= 1088) {
if (!scratch) scratch = std::make_unique_for_overwrite<unsigned[]>(4 * kCapacity);
unsigned *const out[4] = {scratch.get(), scratch.get() + kCapacity, scratch.get() + 2 * kCapacity, scratch.get() + 3 * kCapacity};
const auto parsed = chunk_blocks(p, in.end, count - done, out, emit);
if (!parsed) {
chunks = false;
break;
}
done += parsed;
}
unsigned tail[64];
std::size_t used = 0;
while (done + 2 <= count && in.end - p >= 32) {
const char *next = p;
auto invalid = _mm256_setzero_si256();
const auto groups = two(next, invalid);
if (!_mm256_testz_si256(invalid, invalid)) break;
const auto halves = _mm256_madd_epi16(_mm256_packus_epi32(groups, groups), _mm256_set1_epi32(0x00012710));
const unsigned h0 = _mm256_extract_epi32(halves, 0), l0 = _mm256_extract_epi32(halves, 1);
const unsigned h1 = _mm256_extract_epi32(halves, 4), l1 = _mm256_extract_epi32(halves, 5);
if (h0 > 42 || (h0 == 42 && l0 > 94967295) || h1 > 42 || (h1 == 42 && l1 > 94967295)) break;
tail[used++] = h0 * 100000000 + l0;
tail[used++] = h1 * 100000000 + l1;
if (used == 64) {
emit(tail, used);
used = 0;
}
done += 2;
p = next;
}
if (used) emit(tail, used);
in.current = p;
if (done < count) {
unsigned value = 0;
in.read(value);
emit(&value, 1);
++done;
}
}
}
static void read(FastInput &in, unsigned *out, std::size_t count) {
read_blocks(in, count, [&](const unsigned *values, std::size_t n) {
std::memcpy(out, values, n * sizeof(unsigned));
out += n;
});
}
};
}
#pragma GCC pop_options
#endif
namespace fast_io_detail {
template <class Emit, std::size_t... I>
void emit_record(Emit &emit, const std::uint32_t *values, std::index_sequence<I...>) {
emit(values[I]...);
}
}
template <class Emit>
void read_unsigned_blocks(FastInput &input, std::size_t count, Emit emit) {
#if defined(__linux__) && defined(__x86_64__) && defined(__GNUC__) && !defined(__clang__)
if (__builtin_cpu_supports("avx2")) {
fast_io_detail::BulkInput::read_blocks(input, count, emit);
return;
}
#endif
std::uint32_t values[64];
while (count) {
const auto n = std::min<std::size_t>(count, 64);
for (std::size_t i = 0; i < n; ++i) input.read(values[i]);
emit(values, n);
count -= n;
}
}
inline void read_unsigned(FastInput &input, std::span<std::uint32_t> out) {
read_unsigned_blocks(input, out.size(), [&](const std::uint32_t *values, std::size_t count) {
std::memcpy(out.data(), values, count * sizeof(std::uint32_t));
out = out.subspan(count);
});
}
template <std::size_t Fields, class Emit>
void read_unsigned_records(FastInput &input, std::size_t count, Emit emit) {
static_assert(Fields > 0);
if (count > std::numeric_limits<std::size_t>::max() / Fields) throw std::length_error("input size");
std::array<std::uint32_t, Fields> pending;
std::size_t used = 0;
constexpr auto indices = std::make_index_sequence<Fields>();
read_unsigned_blocks(input, count * Fields, [&](const std::uint32_t *values, std::size_t n) {
std::size_t i = 0;
if (used) {
while (used < Fields && i < n) pending[used++] = values[i++];
if (used == Fields) {
fast_io_detail::emit_record(emit, pending.data(), indices);
used = 0;
}
}
for (; i < n && n - i >= Fields; i += Fields) fast_io_detail::emit_record(emit, values + i, indices);
while (i < n) pending[used++] = values[i++];
});
}
#line 8 "test/convolution_mod.test.cpp"
int main() {
FastInput input;
FastOutput output;
int n = 0, m = 0;
input.read(n);
input.read(m);
std::vector<std::uint32_t> a(n), b(m);
for (auto *values : {&a, &b}) {
std::size_t offset = 0;
read_unsigned_blocks(input, values->size(), [&](const std::uint32_t *block, std::size_t count) {
std::copy(block, block + count, values->data() + offset);
offset += count;
});
}
auto result = convolution_mod(a, b, 1000000007);
write_unsigned_records<1>(output, result.size(), [&](std::size_t i) {
return std::array<std::uint32_t, 1>{result[i]};
});
}