数学计算模板MathCal

namespace MathCal {
  typedef long long LL;
  static const LL mod = 1e9 + 7;
  static const int N = 1e5 + 5;

  LL fac[N], inv[N];

  inline LL pow(LL x, LL exp) {
    LL res = 1;
    for (; exp; exp >>= 1, x = x * x % mod)
      if (exp & 1) res = res * x % mod;
    return res;
  }

  inline void pre() {
    for (int i = fac[0] = 1; i < N; i ++) fac[i] = fac[i - 1] * i % mod;
    inv[N - 1] = pow(fac[N - 1], mod - 2);
    for (int i = N - 1; i; i --) inv[i - 1] = inv[i] * i % mod;
  }

  inline LL Co(int x, int y) {
    return y > x ? 0 : fac[x] * inv[y] % mod * inv[x - y] % mod;
  }
}