verify/verify-yosupo-ntt/yosupo-convolution-schoenhage-radix2.test.cpp

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Last update: 2023-08-10 13:25:59+09:00
Problem: https://judge.yosupo.jp/problem/convolution_mod_1000000007

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"
//
#include "../../template/template.hpp"
//
using namespace Nyaan;

#include "../../modint/montgomery-modint.hpp"
#include "../../ntt/schoenhage-strassen-radix2.hpp"

using mint = LazyMontgomeryModInt<1000000007>;
using vm = V<mint>;
Schoenhage_Strassen_radix2<mint> ss;

/*
#include "misc/timer.hpp"

void calc() {
  int N = TEN(5) * 5;
  vm a(N), b(N);
  int e = 1;
  each(x, a) x = e, ++e;
  each(x, b) x = e, ++e;

  Timer timer;
  auto c = ss.multiply(a, b);
  cerr << c.first.size() << " " << timer.elapsed() << endl;
}

void test() {
  for (int n = 1, m = 1; n < 100; n += 2, m += 2) {
    vm a(n), b(m);
    int e = 1;
    each(x, a) x = e, e += 1;
    // each(x, b) x = e, e += 1;
    b = a;

    auto [c, d] = ss.multiply(a, b);
    mint inv = mint(1 << d).inverse();
    each(x, c) x *= inv;

    vm C(n + m - 1);
    rep(i, n) rep(j, m) C[i + j] += a[i] * b[j];
    assert(C == c);
  }
}
*/

void Nyaan::solve() {
  // test();
  // calc();

  ini(N, M);
  vm a(N), b(M);
  in(a, b);

  auto [c, d] = ss.multiply(a, b);
  mint inv = mint(1 << d).inverse();
  each(x, c) x *= inv;

  out(c);
}

#line 1 "verify/verify-yosupo-ntt/yosupo-convolution-schoenhage-radix2.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/convolution_mod_1000000007"
//
#line 2 "template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
#line 61 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan
#line 64 "template/template.hpp"

// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...)                           \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
#line 70 "template/template.hpp"

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-yosupo-ntt/yosupo-convolution-schoenhage-radix2.test.cpp"
//
using namespace Nyaan;

#line 2 "modint/montgomery-modint.hpp"

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  static_assert(r * mod == 1, "this code has bugs.");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint operator+() const { return mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  constexpr mint inverse() const {
    int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
    while (y > 0) {
      t = x / y;
      x -= t * y, u -= t * v;
      tmp = x, x = y, y = tmp;
      tmp = u, u = v, v = tmp;
    }
    return mint{u};
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
#line 2 "ntt/schoenhage-strassen-radix2.hpp"

template <typename T>
struct Schoenhage_Strassen_radix2 {
  T* buf = nullptr;

  void rot(T* dst, T* src, int s, int d) {
    assert(0 <= d and d < 2 * s);
    bool f = s <= d;
    if (s <= d) d -= s;
    int i = 0;
    if (f) {
      for (; i < s - d; i++) dst[i + d] = -src[i];
      for (; i < s; i++) dst[i + d - s] = src[i];
    } else {
      for (; i < s - d; i++) dst[i + d] = src[i];
      for (; i < s; i++) dst[i + d - s] = -src[i];
    }
  }

  void in_add(T* dst, T* src, int s) {
    for (int i = 0; i < s; i++) dst[i] += src[i];
  }
  void in_sub(T* dst, T* src, int s) {
    for (int i = 0; i < s; i++) dst[i] -= src[i];
  }

  void cp(T* dst, T* src, int s) { memcpy(dst, src, s * sizeof(T)); }
  void reset(T* dst, int s) { fill(dst, dst + s, T()); }

  // R[x] / (1 + x^(2^m)) 上の長さ2^LのFFT
  void fft(T* a, int l, int m) {
    if (l == 0) return;
    int L = 1 << l, M = 1 << m;
    assert(M * 2 >= L);
    assert(buf != nullptr);

    vector<int> dw(l - 1);
    for (int i = 0; i < l - 1; i++) {
      dw[i] = (1 << (l - 2 - i)) + (1 << (l - 1 - i)) - (1 << (l - 1));
      if (dw[i] < 0) dw[i] += L;
      if (L == M) dw[i] *= 2;
      if (2 * L == M) dw[i] *= 4;
    }

    for (int d = L; d >>= 1;) {
      int w = 0;
      for (int s = 0, k = 0;;) {
        for (int i = s, j = s + d; i < s + d; ++i, ++j) {
          T *ai = a + i * M, *aj = a + j * M;
          rot(buf, aj, M, w);
          cp(aj, ai, M);
          in_add(ai, buf, M);
          in_sub(aj, buf, M);
        }
        if ((s += 2 * d) >= L) break;
        w += dw[__builtin_ctz(++k)];
        if (w >= 2 * M) w -= 2 * M;
      }
    }
  }

  // R[x] / (1 + x^(2^m)) 上の長さ2^LのIFFT
  void ifft(T* a, int l, int m) {
    if (l == 0) return;
    int L = 1 << l, M = 1 << m;
    assert(M * 2 >= L);
    assert(buf != nullptr);

    vector<int> dw(l - 1);
    for (int i = 0; i < l - 1; i++) {
      dw[i] = (1 << (l - 2 - i)) + (1 << (l - 1 - i)) - (1 << (l - 1));
      if (dw[i] < 0) dw[i] += L;
      if (L == M) dw[i] *= 2;
      if (2 * L == M) dw[i] *= 4;
    }

    for (int d = 1; d < L; d *= 2) {
      int w = 0;
      for (int s = 0, k = 0;;) {
        for (int i = s, j = s + d; i < s + d; ++i, ++j) {
          T *ai = a + i * M, *aj = a + j * M;
          cp(buf, ai, M);
          in_add(ai, aj, M);
          in_sub(buf, aj, M);
          rot(aj, buf, M, w);
        }
        if ((s += 2 * d) >= L) break;
        w -= dw[__builtin_ctz(++k)];
        if (w < 0) w += 2 * M;
      }
    }
  }

  // a <- ab / (x^(2^n)+1)
  int naive_mul(T* a, T* b, int n) {
    int N = 1 << n;
    reset(buf, N);
    for (int i = 0; i < N; i++) {
      int j = 0;
      for (; j < N - i; j++) buf[i + j] += a[i] * b[j];
      for (; j < N; j++) buf[i + j - N] -= a[i] * b[j];
    }
    cp(a, buf, N);
    return 0;
  }

  // a <- ab / (x^(2^n)+1)
  int inplace_mul(T* a, T* b, int n) {
    if (n <= 5) {
      naive_mul(a, b, n);
      return 0;
    }

    int l = (n + 1) / 2;
    int m = n / 2;
    int L = 1 << l, M = 1 << m, N = 1 << n;
    int cnt = 0;

    // R[x] (x^(2^(m+1))-1) R[y] (y^(2^l)-1)
    vector<T> A(N * 2), B(N * 2);
    reset(buf + M, M);
    for (int i = 0, s = 0, ds = 2 * M / L; i < L; i++) {
      // y -> x^{2m/r} y
      cp(buf, a + i * M, M);
      rot(A.data() + i * M * 2, buf, 2 * M, s);
      cp(buf, b + i * M, M);
      rot(B.data() + i * M * 2, buf, 2 * M, s);
      s += ds;
      if (s >= 4 * M) s -= 4 * M;
    }

    fft(A.data(), l, m + 1);
    fft(B.data(), l, m + 1);
    for (int i = 0; i < L; i++) {
      cnt = inplace_mul(A.data() + i * M * 2, B.data() + i * M * 2, m + 1);
    }
    ifft(A.data(), l, m + 1);

    for (int i = 0, s = 0, ds = 2 * M / L; i < L; i++) {
      // y -> x^{-2m/r} y
      cp(buf, A.data() + i * M * 2, 2 * M);
      rot(A.data() + i * M * 2, buf, 2 * M, s);
      s -= ds;
      if (s < 0) s += 4 * M;
    }

    for (int i = 0; i < L; i++) {
      for (int j = 0; j < M; j++) {
        a[i * M + j] = A[i * M * 2 + j];
        if (i == 0) {
          a[i * M + j] -= A[(L - 1) * M * 2 + M + j];
        } else {
          a[i * M + j] += A[(i - 1) * M * 2 + M + j];
        }
      }
    }
    return cnt + l;
  }

  // a <- ab / (x^(2^n)-1)
  int inplace_mul2(T* a, T* b, int n) {
    if (n <= 5) {
      naive_mul(a, b, n);
      return 0;
    }

    int l = (n + 1) / 2;
    int m = n / 2;
    int L = 1 << l, M = 1 << m, N = 1 << n;
    int cnt = 0;

    // R[x] (x^(2^(m+1))-1) R[y] (y^(2^l)-1)
    vector<T> A(N * 2), B(N * 2);
    for (int i = 0; i < L; i++) {
      cp(A.data() + i * M * 2, a + i * M, M);
      cp(B.data() + i * M * 2, b + i * M, M);
    }
    fft(A.data(), l, m + 1);
    fft(B.data(), l, m + 1);
    for (int i = 0; i < L; i++) {
      cnt = inplace_mul(A.data() + i * M * 2, B.data() + i * M * 2, m + 1);
    }
    ifft(A.data(), l, m + 1);
    for (int i = 0; i < L; i++) {
      for (int j = 0; j < M; j++) {
        a[i * M + j] = A[i * M * 2 + j];
        a[i * M + j] += A[(i ? i - 1 : L - 1) * M * 2 + M + j];
      }
    }
    return cnt + l;
  }

  pair<vector<T>, int> multiply(const vector<T>& a, const vector<T>& b) {
    int L = a.size() + b.size() - 1;
    int M = 1, m = 0;
    while (M < L) M *= 2, m++;
    buf = new T[M];
    vector<T> s(M), t(M);
    for (int i = 0; i < (int)a.size(); i++) s[i] = a[i];
    for (int i = 0; i < (int)b.size(); i++) t[i] = b[i];
    int cnt = inplace_mul2(s.data(), t.data(), m);
    vector<T> u(L);
    for (int i = 0; i < L; i++) u[i] = s[i];
    delete[] buf;
    return make_pair(u, cnt);
  }
};

/**
 * @brief Schönhage-Strassen Algorithm(radix-2)
 */
#line 9 "verify/verify-yosupo-ntt/yosupo-convolution-schoenhage-radix2.test.cpp"

using mint = LazyMontgomeryModInt<1000000007>;
using vm = V<mint>;
Schoenhage_Strassen_radix2<mint> ss;

/*
#include "misc/timer.hpp"

void calc() {
  int N = TEN(5) * 5;
  vm a(N), b(N);
  int e = 1;
  each(x, a) x = e, ++e;
  each(x, b) x = e, ++e;

  Timer timer;
  auto c = ss.multiply(a, b);
  cerr << c.first.size() << " " << timer.elapsed() << endl;
}

void test() {
  for (int n = 1, m = 1; n < 100; n += 2, m += 2) {
    vm a(n), b(m);
    int e = 1;
    each(x, a) x = e, e += 1;
    // each(x, b) x = e, e += 1;
    b = a;

    auto [c, d] = ss.multiply(a, b);
    mint inv = mint(1 << d).inverse();
    each(x, c) x *= inv;

    vm C(n + m - 1);
    rep(i, n) rep(j, m) C[i + j] += a[i] * b[j];
    assert(C == c);
  }
}
*/

void Nyaan::solve() {
  // test();
  // calc();

  ini(N, M);
  vm a(N), b(M);
  in(a, b);

  auto [c, d] = ss.multiply(a, b);
  mint inv = mint(1 << d).inverse();
  each(x, c) x *= inv;

  out(c);
}

Nyaan's Library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/verify-yosupo-ntt/yosupo-convolution-schoenhage-radix2.test.cpp

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