結果

問題 No.940 ワープ　ε=ε=ε=ε=ε=│;p>д＜│
ユーザー 👑 hos.lyrichos.lyric
提出日時 2019-12-03 01:11:56
言語 C++14
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 2,623 ms / 5,000 ms
コード長 7,499 bytes
コンパイル時間 1,279 ms
コンパイル使用メモリ 110,872 KB
実行使用メモリ 147,012 KB
最終ジャッジ日時 2023-08-18 23:22:27
合計ジャッジ時間 17,593 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge12
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 85 ms
63,104 KB
testcase_01 AC 95 ms
63,168 KB
testcase_02 AC 89 ms
63,168 KB
testcase_03 AC 93 ms
63,352 KB
testcase_04 AC 85 ms
63,100 KB
testcase_05 AC 88 ms
63,372 KB
testcase_06 AC 86 ms
63,420 KB
testcase_07 AC 85 ms
63,176 KB
testcase_08 AC 84 ms
63,148 KB
testcase_09 AC 85 ms
63,316 KB
testcase_10 AC 89 ms
63,304 KB
testcase_11 AC 85 ms
63,316 KB
testcase_12 AC 89 ms
63,448 KB
testcase_13 AC 94 ms
63,260 KB
testcase_14 AC 91 ms
63,204 KB
testcase_15 AC 182 ms
68,080 KB
testcase_16 AC 299 ms
75,316 KB
testcase_17 AC 1,117 ms
104,048 KB
testcase_18 AC 1,119 ms
106,456 KB
testcase_19 AC 1,104 ms
103,876 KB
testcase_20 AC 1,098 ms
109,804 KB
testcase_21 AC 498 ms
84,628 KB
testcase_22 AC 1,127 ms
109,060 KB
testcase_23 AC 493 ms
83,584 KB
testcase_24 AC 1,142 ms
109,468 KB
testcase_25 AC 2,544 ms
145,060 KB
testcase_26 AC 2,623 ms
147,012 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }

// a^-1 (mod m)
//   m > 0
Int modInv(Int a, Int m) {
  Int b = m, x = 1, y = 0, t;
  for (; ; ) {
    t = a / b; a -= t * b;
    if (a == 0) {
      assert(b == 1 || b == -1);
      if (b == -1) y = -y;
      return (y < 0) ? (y + m) : y;
    }
    x -= t * y;
    t = b / a; b -= t * a;
    if (b == 0) {
      assert(a == 1 || a == -1);
      if (a == -1) x = -x;
      return (x < 0) ? (x + m) : x;
    }
    y -= t * x;
  }
}

// M: prime, G: primitive root
template <int M, int G, int K> struct Fft {
  // 1, 1/4, 1/8, 3/8, 1/16, 5/16, 3/16, 7/16, ...
  int g[1 << (K - 1)];
  /*constexpr*/ Fft() : g() {
    static_assert(K >= 2, "Fft: K >= 2 must hold");
    static_assert(!((M - 1) & ((1 << K) - 1)), "Fft: 2^K | M - 1 must hold");
    g[0] = 1;
    long long g2 = G, gg = 1;
    for (int e = (M - 1) >> K; e; e >>= 1) {
      if (e & 1) gg = (gg * g2) % M;
      g2 = (g2 * g2) % M;
    }
    g[1 << (K - 2)] = gg;
    for (int l = 1 << (K - 2); l >= 2; l >>= 1) {
      g[l >> 1] = (static_cast<long long>(g[l]) * g[l]) % M;
    }
    assert((static_cast<long long>(g[1]) * g[1]) % M == M - 1);
    for (int l = 2; l <= 1 << (K - 2); l <<= 1) {
      for (int i = 1; i < l; ++i) {
        g[l + i] = (static_cast<long long>(g[l]) * g[i]) % M;
      }
    }
  }
  void fft(vector<int> &x) const {
    const int n = x.size();
    assert(!(n & (n - 1)) && n <= 1 << K);
    for (int l = n; l >>= 1; ) {
      for (int i = 0; i < (n >> 1) / l; ++i) {
        for (int j = (i << 1) * l; j < (i << 1 | 1) * l; ++j) {
          const int t = (static_cast<long long>(g[i]) * x[j + l]) % M;
          if ((x[j + l] = x[j] - t) < 0) x[j + l] += M;
          if ((x[j] += t) >= M) x[j] -= M;
        }
      }
    }
    for (int i = 0, j = 0; i < n; ++i) {
      if (i < j) std::swap(x[i], x[j]);
      for (int l = n; (l >>= 1) && !((j ^= l) & l); ) {}
    }
  }
  vector<int> convolution(const vector<int> &a, const vector<int> &b) const {
    const int na = a.size(), nb = b.size();
    int n, invN = 1;
    for (n = 1; n < na + nb - 1; n <<= 1) invN = ((invN & 1) ? (invN + M) : invN) >> 1;
    vector<int> x(n, 0), y(n, 0);
    std::copy(a.begin(), a.end(), x.begin());
    std::copy(b.begin(), b.end(), y.begin());
    fft(x);
    fft(y);
    for (int i = 0; i < n; ++i) x[i] = (((static_cast<long long>(x[i]) * y[i]) % M) * invN) % M;
    std::reverse(x.begin() + 1, x.end());
    fft(x);
    x.resize(na + nb - 1);
    return x;
  }
};


template<int M_> struct ModInt {
  static constexpr int M = M_;
  int x;
  constexpr ModInt() : x(0) {}
  constexpr ModInt(long long x_) : x(x_ % M) { if (x < 0) x += M; }
  ModInt &operator+=(const ModInt &a) { x += a.x; if (x >= M) x -= M; return *this; }
  ModInt &operator-=(const ModInt &a) { x -= a.x; if (x < 0) x += M; return *this; }
  ModInt &operator*=(const ModInt &a) { x = static_cast<int>((static_cast<long long>(x) * a.x) % M); return *this; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator-() const { return ModInt(-x); }
  ModInt pow(long long e) const {
    ModInt x2 = x, xe = 1;
    for (; e; e >>= 1) {
      if (e & 1) xe *= x2;
      x2 *= x2;
    }
    return xe;
  }
  ModInt inv() const {
    int a = x, b = M, y = 1, z = 0, t;
    for (; ; ) {
      t = a / b; a -= t * b;
      if (a == 0) {
        assert(b == 1 || b == -1);
        return ModInt(b * z);
      }
      y -= t * z;
      t = b / a; b -= t * a;
      if (b == 0) {
        assert(a == 1 || a == -1);
        return ModInt(a * y);
      }
      z -= t * y;
    }
  }
  friend ModInt operator+(long long a, const ModInt &b) { return (ModInt(a) += b); }
  friend ModInt operator-(long long a, const ModInt &b) { return (ModInt(a) -= b); }
  friend ModInt operator*(long long a, const ModInt &b) { return (ModInt(a) *= b); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};

constexpr Int MO = 1'000'000'007;
using Mint = ModInt<MO>;

constexpr int LIM = 3'000'000;
Mint inv[LIM], fac[LIM], invFac[LIM];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM; ++i) {
    inv[i] = -(Mint::M / i) * inv[Mint::M % i];
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (0 <= k && k <= n) {
    assert(n < LIM);
    return fac[n] * invFac[k] * invFac[n - k];
  } else {
    return 0;
  }
}


constexpr Int FFT_P0 = 469762049;  // 2^26 7 + 1
constexpr Int FFT_P1 = 167772161;  // 2^25 5 + 1
constexpr Int FFT_P2 = 754974721;  // 2^24 45 + 1
const Fft<FFT_P0, 3, 22> FFT0;
const Fft<FFT_P1, 3, 22> FFT1;
const Fft<FFT_P2, 11, 22> FFT2;

vector<Mint> multiply(const vector<Mint> &a, const vector<Mint> &b) {
  const Int FFT_INV01 = modInv(FFT_P0, FFT_P1);
  const Int FFT_INV012 = modInv(FFT_P0 * FFT_P1, FFT_P2);
  vector<int> aa(a.size()), bb(b.size());
  for (size_t i = 0; i < a.size(); ++i) aa[i] = a[i].x % FFT_P0;
  for (size_t i = 0; i < b.size(); ++i) bb[i] = b[i].x % FFT_P0;
  const vector<int> x0 = FFT0.convolution(aa, bb);
  for (size_t i = 0; i < a.size(); ++i) aa[i] = a[i].x % FFT_P1;
  for (size_t i = 0; i < b.size(); ++i) bb[i] = b[i].x % FFT_P1;
  const vector<int> x1 = FFT1.convolution(aa, bb);
  for (size_t i = 0; i < a.size(); ++i) aa[i] = a[i].x % FFT_P2;
  for (size_t i = 0; i < b.size(); ++i) bb[i] = b[i].x % FFT_P2;
  const vector<int> x2 = FFT2.convolution(aa, bb);
  vector<Mint> x(x0.size());
  for (size_t i = 0; i < x0.size(); ++i) {
    Int y0 = x0[i] % FFT_P0;
    Int y1 = (FFT_INV01 * (x1[i] - y0)) % FFT_P1;
    if (y1 < 0) {
      y1 += FFT_P1;
    }
    Int y2 = (FFT_INV012 * ((x2[i] - y0 - FFT_P0 * y1) % FFT_P2)) % FFT_P2;
    if (y2 < 0) {
      y2 += FFT_P2;
    }
    x[i] = Mint(1) * y0 + Mint(FFT_P0) * y1 + Mint(FFT_P0 * FFT_P1) * y2;
  }
  return x;
}


int main() {
  prepare();
  int X, Y, Z;
  for (; ~scanf("%d%d%d", &X, &Y, &Z); ) {
    const int n = X + Y + Z;
    if (n == 0) {
      puts("1");
      continue;
    }
    vector<Mint> a(n + 1), b(n + 1);
    for (int i = 0; i <= n; ++i) {
      a[i] = invFac[i] * binom(X + i - 1, i - 1) * binom(Y + i - 1, i - 1) * binom(Z + i - 1, i - 1);
      b[i] = ((i % 2 != 0) ? -1 : +1) * invFac[i];
    }
    const vector<Mint> res = multiply(a, b);
    Mint ans = 0;
    for (int i = 0; i <= n; ++i) {
      ans += fac[i] * res[i];
    }
    printf("%d\n", ans.x);
  }
  return 0;
}
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