結果

問題 No.3046 yukicoderの過去問
ユーザー risujirohrisujiroh
提出日時 2019-04-02 10:20:28
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 295 ms / 2,000 ms
コード長 6,020 bytes
コンパイル時間 2,376 ms
コンパイル使用メモリ 186,940 KB
実行使用メモリ 36,368 KB
最終ジャッジ日時 2024-05-06 16:06:31
合計ジャッジ時間 4,565 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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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 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 214 ms
34,784 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 249 ms
35,748 KB
testcase_06 AC 295 ms
35,840 KB
testcase_07 AC 287 ms
36,368 KB
testcase_08 AC 291 ms
35,996 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;

template<unsigned P> struct ModInt {
  using M = ModInt;
  unsigned v;
  ModInt() : v(0) {}
  template<class Z> ModInt(Z x) : v(x >= 0 ? x % P : (P - -x % P) % P) {}
  constexpr ModInt(unsigned v, int) : v(v) {}
  static constexpr unsigned p() { return P; }
  M operator+() const { return *this; }
  M operator-() const { return {v ? P - v : 0, 0}; }
  explicit operator bool() const noexcept { return v; }
  bool operator!() const noexcept { return !(bool) *this; }
  M operator*(M r) const { return M(*this) *= r; }
  M operator/(M r) const { return M(*this) /= r; }
  M operator+(M r) const { return M(*this) += r; }
  M operator-(M r) const { return M(*this) -= r; }
  bool operator==(M r) const { return v == r.v; }
  bool operator!=(M r) const { return !(*this == r); }
  M& operator*=(M r) { v = (uint64_t) v * r.v % P; return *this; }
  M& operator/=(M r) { return *this *= r.inv(); }
  M& operator+=(M r) { if ((v += r.v) >= P) v -= P; return *this; }
  M& operator-=(M r) { if ((v += P - r.v) >= P) v -= P; return *this; }
  M inv() const {
    int a = v, b = P, x = 1, u = 0;
    while (b) {
      int q = a / b;
      swap(a -= q * b, b);
      swap(x -= q * u, u);
    }
    assert(a == 1);
    return x;
  }
  template<class Z> M pow(Z n) const {
    if (n < 0) return pow(-n).inv();
    M res = 1;
    for (M a = *this; n; a *= a, n >>= 1) if (n & 1) res *= a;
    return res;
  }
  template<class Z> friend M operator*(Z l, M r) { return M(l) *= r; }
  template<class Z> friend M operator/(Z l, M r) { return M(l) /= r; }
  template<class Z> friend M operator+(Z l, M r) { return M(l) += r; }
  template<class Z> friend M operator-(Z l, M r) { return M(l) -= r; }
  friend ostream& operator<<(ostream& os, M r) { return os << r.v; }
  friend istream& operator>>(istream& is, M& r) { lint x; is >> x; r = x; return is; }
  template<class Z> friend bool operator==(Z l, M r) { return M(l) == r; }
  template<class Z> friend bool operator!=(Z l, M r) { return !(l == r); }
};
using Mint = ModInt<(unsigned) 1e9 + 7>;

using R = double;
constexpr R pi = acos((R) -1);
using C = complex<R>;
C& operator*=(C& l, const C& r) {
  return l = {real(l) * real(r) - imag(l) * imag(r), real(l) * imag(r) + imag(l) * real(r)};
}
void fft(V<C>& a, bool inv = false) {
  int n = a.size();
  int j = 0;
  for (int i = 1; i < n; ++i) {
    int w = n >> 1;
    while (j >= w) j -= w, w >>= 1;
    j += w;
    if (i < j) swap(a[i], a[j]);
  }
  static VV<C> xi(30);
  for (int k = 0; 1 << k < n; ++k) if (xi[k].empty()) {
    xi[k].resize(1 << k);
    for (int i = 0; i < 1 << k; ++i) {
      xi[k][i] = polar<R>(1, i * pi / (1 << k));
    }
  }
  for (int k = 0; 1 << k < n; ++k) {
    const int w = 1 << k;
    for (int s = 0; s < n; s += 2 * w) {
      for (int i = s; i < s + w; ++i) {
        j = i + w;
        a[j] *= inv ? conj(xi[k][i - s]) : xi[k][i - s];
        tie(a[i], a[j]) = make_pair(a[i] + a[j], a[i] - a[j]);
      }
    }
  }
}
// BEGIN CUT HERE
template<int K = 15> void multiply(V<Mint>& a, const V<Mint>& b) {
  assert(!a.empty() and !b.empty());
  int n = 1 << __lg(2 * (a.size() + b.size() - 1) - 1);
  V<C> f(n), g(n);
  for (int i = 0; i < n; ++i) {
    if (i < (int) a.size()) f[i].real(a[i].v & ~(~0 << K)), f[i].imag(a[i].v >> K);
    if (i < (int) b.size()) g[i].real(b[i].v & ~(~0 << K)), g[i].imag(b[i].v >> K);
  }
  fft(f), fft(g);
  V<C> Al(n), Au(n), Bl(n), Bu(n);
  for (int i = 0; i < n; ++i) {
    Al[i] = (f[i] + conj(f[-i & n - 1])) / C(2, 0);
    Au[i] = (f[i] - conj(f[-i & n - 1])) / C(0, 2);
    Bl[i] = (g[i] + conj(g[-i & n - 1])) / C(2, 0);
    Bu[i] = (g[i] - conj(g[-i & n - 1])) / C(0, 2);
  }
  for (int i = 0; i < n; ++i) {
    f[i] = Al[i] * Bl[i] + C(0, 1) * Al[i] * Bu[i];
    g[i] = Au[i] * Bl[i] + C(0, 1) * Au[i] * Bu[i];
  }
  fft(f, true), fft(g, true);
  a.resize(a.size() + b.size() - 1);
  for (int i = 0; i < (int) a.size(); ++i) {
    lint l = real(f[i]) / n + 0.5;
    lint m = (imag(f[i]) + real(g[i])) / n + 0.5;
    lint u = imag(g[i]) / n + 0.5;
    a[i] = l + m * Mint(1 << K) + u * Mint(1 << 2 * K);
  }
}
// END CUT HERE

template<class T> struct Polynomial {
  using P = Polynomial;
  V<T> c;
  Polynomial(int n = 0) : c(n) {}
  void shrink() { while (!c.empty() and !c.back()) c.pop_back(); }
  int size() const { return c.size(); }
  T& operator[](int i) { return c[i]; }
  const T& operator[](int i) const { return c[i]; }
  P operator*(const P& r) const { return P(*this) *= r; }
  P operator*(const T& 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; }
  P operator-(const P& r) const { return P(*this) -= r; }
  P& operator*=(const T& r) {
    for (int i = 0; i < size(); ++i) c[i] *= r;
    shrink();
    return *this;
  }
  P& operator*=(const P& r) { multiply(c, r.c), shrink(); return *this; }
  P& operator/=(const P& r) { return *this *= r.inverse(); }
  P& operator+=(const P& r) {
    if (r.size() > size()) c.resize(r.size());
    for (int i = 0; i < r.size(); ++i) c[i] += r[i];
    shrink();
    return *this;
  }
  P& operator-=(const P& r) {
    if (r.size() > size()) c.resize(r.size());
    for (int i = 0; i < r.size(); ++i) c[i] -= r[i];
    shrink();
    return *this;
  }
  P inverse(int n) const {
    if (n == 1) {
      assert(!c.empty());
      P res(1);
      res[0] = 1 / c[0];
      return res;
    }
    P res = *this;
    res.c.resize(n);
    P inv = res.inverse(n + 1 >> 1);
    res = inv * (T) 2 - res * inv * inv;
    res.c.resize(n);
    res.shrink();
    return res;
  }
};
using P = Polynomial<Mint>;

int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);
  int k, n; cin >> k >> n;
  P f(1e5 + 1);
  f[0] = 1;
  for (int i = 0; i < n; ++i) {
    int x; cin >> x;
    f[x] = -1;
  }
  f.shrink();
  cout << f.inverse(k + 1)[k] << '\n';
}
0