結果

問題 No.3046 yukicoderの過去問
ユーザー pekempeypekempey
提出日時 2019-04-03 06:53:27
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 382 ms / 2,000 ms
コード長 6,346 bytes
コンパイル時間 1,486 ms
コンパイル使用メモリ 97,024 KB
実行使用メモリ 62,240 KB
最終ジャッジ日時 2024-05-09 16:52:38
合計ジャッジ時間 3,959 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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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 22 ms
19,932 KB
testcase_01 AC 21 ms
20,096 KB
testcase_02 AC 21 ms
20,156 KB
testcase_03 AC 280 ms
41,976 KB
testcase_04 AC 22 ms
20,112 KB
testcase_05 AC 367 ms
61,880 KB
testcase_06 AC 382 ms
62,240 KB
testcase_07 AC 379 ms
62,124 KB
testcase_08 AC 382 ms
62,128 KB
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ソースコード

diff # 

#include <iostream>
#include <algorithm>
#include <vector>
#include <complex>

using namespace std;

const int MOD = 1e9 + 7;

struct mint {
  int n;
  mint(int n_ = 0) : n(n_) {}
};

mint operator-(mint a) { return a.n == 0 ? 0 : MOD - a.n; }
mint operator+(mint a, mint b) { return (a.n += b.n) >= MOD ? a.n - MOD : a.n; }
mint operator-(mint a, mint b) { return (a.n -= b.n) < 0 ? a.n + MOD : a.n; }
mint operator*(mint a, mint b) { return 1LL * a.n * b.n % MOD; }
mint &operator+=(mint &a, mint b) { return a = a + b; }
mint &operator-=(mint &a, mint b) { return a = a - b; }
mint &operator*=(mint &a, mint b) { return a = a * b; }
ostream &operator<<(ostream &o, mint a) { return o << a.n; }

mint modpow(mint a, long long b) {
  mint res = 1;
  while (b > 0) {
    if (b & 1) res *= a;
    a *= a;
    b >>= 1;
  }
  return res;
}

mint modinv(mint a) {
  return modpow(a, MOD - 2);
}

template<int N>
struct FFT {
  complex<double> rots[N];

  FFT() {
    const double pi = acos(-1);
    for (int i = 0; i < N / 2; i++) {
      rots[i + N / 2].real(cos(2 * pi / N * i));
      rots[i + N / 2].imag(sin(2 * pi / N * i));
    }
    for (int i = N / 2 - 1; i >= 1; i--) {
      rots[i] = rots[i * 2];
    }
  }

  inline complex<double> mul(complex<double> a, complex<double> b) {
    return complex<double>(
        a.real() * b.real() - a.imag() * b.imag(),
        a.real() * b.imag() + a.imag() * b.real()
        );
  }

  void fft(vector<complex<double>> &a, bool rev) {
    const int n = a.size();
    int i = 0;
    for (int j = 1; j < n - 1; j++) {
      for (int k = n >> 1; k > (i ^= k); k >>= 1);
      if (j < i) {
        swap(a[i], a[j]);
      }
    }
    for (int i = 1; i < n; i *= 2) {
      for (int j = 0; j < n; j += i * 2) {
        for (int k = 0; k < i; k++) {
          auto s = a[j + k + 0];
          auto t = mul(a[j + k + i], rots[i + k]);
          a[j + k + 0] = s + t;
          a[j + k + i] = s - t;
        }
      }
    }
    if (rev) {
      reverse(a.begin() + 1, a.end());
      for (int i = 0; i < n; i++) {
        a[i] *= 1.0 / n;
      }
    }
  }

  vector<long long> convolution(vector<long long> a, vector<long long> b) {
    int t = 1;
    while (t < a.size() + b.size() - 1) t *= 2;
    vector<complex<double>> z(t);
    for (int i = 0; i < a.size(); i++) z[i].real(a[i]);
    for (int i = 0; i < b.size(); i++) z[i].imag(b[i]);
    fft(z, false);
    vector<complex<double>> w(t);
    for (int i = 0; i < t; i++) {
      auto p = (z[i] + conj(z[(t - i) % t])) * complex<double>(0.5, 0);
      auto q = (z[i] - conj(z[(t - i) % t])) * complex<double>(0, -0.5);
      w[i] = p * q;
    }
    fft(w, true);
    vector<long long> ans(a.size() + b.size() - 1);
    for (int i = 0; i < ans.size(); i++) {
      ans[i] = round(w[i].real());
    }
    return ans;
  }

  vector<mint> convolution(vector<mint> a, vector<mint> b) {
    int t = 1;
    while (t < a.size() + b.size() - 1) t *= 2;
    vector<complex<double>> A(t), B(t);
    for (int i = 0; i < a.size(); i++) A[i] = complex<double>(a[i].n & 0x7fff, a[i].n >> 15);
    for (int i = 0; i < b.size(); i++) B[i] = complex<double>(b[i].n & 0x7fff, b[i].n >> 15);
    fft(A, false);
    fft(B, false);
    vector<complex<double>> C(t), D(t);
    for (int i = 0; i < t; i++) {
      int j = (t - i) % t;
      auto AL = (A[i] + conj(A[j])) * complex<double>(0.5, 0);
      auto AH = (A[i] - conj(A[j])) * complex<double>(0, -0.5);
      auto BL = (B[i] + conj(B[j])) * complex<double>(0.5, 0);
      auto BH = (B[i] - conj(B[j])) * complex<double>(0, -0.5);
      C[i] = AL * BL + AH * BL * complex<double>(0, 1);
      D[i] = AL * BH + AH * BH * complex<double>(0, 1);
    }
    fft(C, true);
    fft(D, true);
    vector<mint> ans(a.size() + b.size() - 1);
    for (int i = 0; i < ans.size(); i++) {
      long long l = (long long)round(C[i].real()) % MOD;
      long long m = ((long long)round(C[i].imag()) + (long long)round(D[i].real())) % MOD;
      long long h = (long long)round(D[i].imag()) % MOD;
      ans[i] = (l + (m << 15) + (h << 30)) % MOD;
    }
    return ans;
  }
};
FFT<1 << 20> fft;

typedef vector<mint> poly; 

poly operator-(poly a) {
  for (int i = 0; i < a.size(); i++) {
    a[i] = -a[i];
  }
  return a;
}

poly operator+(poly a, poly b) {
  if (a.size() < b.size()) a.resize(b.size());
  for (int i = 0; i < b.size(); i++) {
    a[i] += b[i];
  }
  return a;
}

poly operator-(poly a, poly b) {
  if (a.size() < b.size()) a.resize(b.size());
  for (int i = 0; i < b.size(); i++) {
    a[i] -= b[i];
  }
  return a;
}

poly operator*(poly a, poly b) {
  return fft.convolution(a, b);
}

poly &operator+=(poly &a, poly b) { return a = a + b; }
poly &operator-=(poly &a, poly b) { return a = a - b; }

poly pinv(poly a) {
  const int n = a.size();
  poly x = {modinv(a[0])};
  for (int i = 1; i < n; i *= 2) {
    vector<mint> tmp(min(i * 2, n));
    for (int j = 0; j < tmp.size(); j++) {
      tmp[j] = a[j];
    }
    auto e = -fft.convolution(tmp, x);
    e[0] += 2;
    x = fft.convolution(x, e);
    x.resize(i * 2);
  }
  x.resize(n);
  return x;
}

poly plog(poly a) {
  const int n = a.size();
  vector<mint> b(n);
  for (int i = 1; i < n; i++) {
    b[i - 1] = i * a[i];
  }
  a = fft.convolution(pinv(a), b);
  for (int i = n - 1; i >= 1; i--) {
    a[i] = modinv(i) * a[i - 1];
  }
  a[0] = 0;
  a.resize(n);
  return a;
}

poly pexp(poly a) {
  const int n = a.size();
  poly x = {1};
  for (int i = 1; i < n; i *= 2) {
    auto e = -plog(x);
    e[0] += 1;
    e.resize(min(i * 2, n));
    for (int j = 0; j < e.size(); j++) {
      e[j] += a[j];
    }
    x = fft.convolution(x, e);
    x.resize(i * 2);
  }
  x.resize(n);
  return x;
}

poly quot(poly a, poly b) {
  if (a.size() < b.size()) return {};
  reverse(a.begin(), a.end());
  reverse(b.begin(), b.end());
  int n = a.size();
  int m = b.size();
  b.resize(n - m + 1);
  a = a * pinv(b);
  a.resize(n - m + 1);
  reverse(a.begin(), a.end());
  return a;
}

poly rem(poly a, poly b) {
  return a - quot(a, b) * b;
}

int main() {
  int K, N;
  cin >> K >> N;
  vector<int> A(N);
  for (int i = 0; i < N; i++) {
    scanf("%d", &A[i]);
  }
  int M = A.back();
  poly Y(M + 1);
  Y[M] = 1;
  for (int i = 0; i < N; i++) {
    Y[M - A[i]] = MOD - 1;
  }
  poly X(M - 1 + K + 1);
  X[M - 1 + K] = 1;
  X = rem(X, Y);
  cout << X[M - 1].n << '\n';
}
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