結果

問題 No.665 Bernoulli Bernoulli
ユーザー 👑 hos.lyric
提出日時 2019-05-02 06:51:36
言語 D
(dmd 2.109.1)
結果
AC  
実行時間 50 ms / 2,000 ms
コード長 3,680 bytes
コンパイル時間 932 ms
コンパイル使用メモリ 121,036 KB
実行使用メモリ 29,660 KB
最終ジャッジ日時 2024-06-22 01:05:28
合計ジャッジ時間 2,621 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
sample AC * 4
other AC * 15
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ソースコード

diff #
プレゼンテーションモードにする

import std.conv, std.functional, std.range, std.stdio, std.string;
import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, std.numeric, std.regex, std.typecons;
import core.bitop;
class EOFException : Throwable { this() { super("EOF"); } }
string[] tokens;
string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens
    .popFront; return token; }
int readInt() { return readToken.to!int; }
long readLong() { return readToken.to!long; }
real readReal() { return readToken.to!real; }
bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }
bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }
int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; 
    (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }
int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }
int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }
// a^-1 (mod m)
long modInv(long a, long m)
in {
  assert(m > 0, "modInv: m > 0 must hold");
}
do {
  long b = m, x = 1, y = 0, t;
  for (; ; ) {
    t = a / b;
    a -= t * b;
    if (a == 0) {
      assert(b == 1 || b == -1, "modInv: gcd(a, m) != 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, "modInv: gcd(a, m) != 1");
      if (a == -1) {
        x = -x;
      }
      return (x < 0) ? (x + m) : x;
    }
    y -= t * x;
  }
}
enum MO = 10L^^9 + 7;
enum LIM = 10^^6;
long[] inv, fac, invFac;
void prepare() {
  inv = new long[LIM];
  fac = new long[LIM];
  invFac = new long[LIM];
  inv[1] = 1;
  foreach (i; 2 .. LIM) {
    inv[i] = MO - ((MO / i) * inv[cast(size_t)(MO % i)]) % MO;
  }
  fac[0] = invFac[0] = 1;
  foreach (i; 1 .. LIM) {
    fac[i] = (fac[i - 1] * i) % MO;
    invFac[i] = (invFac[i - 1] * inv[i]) % MO;
  }
}
long binom(long n, long k) {
  if (0 <= k && k <= n) {
    assert(n < LIM);
    return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] % MO * invFac[cast(size_t)(n - k)] % MO;
  } else {
    return 0;
  }
}
long power(long a, long e) {
  long x = a % MO, y = 1;
  for (; e; e >>= 1) {
    if (e & 1) {
      y = (y * x) % MO;
    }
    x = (x * x) % MO;
  }
  return y;
}
long N;
int K;
void main() {
  prepare();
  try {
    for (; ; ) {
      N = readLong();
      K = readInt();
      
      auto f = new long[K + 2];
      f[0] = 0;
      foreach (i; 1 .. K + 2) {
        f[i] = (f[i - 1] + power(i, K)) % MO;
      }
      
      bool zero;
      long prod = 1;
      foreach (i; 0 .. K + 2) {
        const d = (N - i) % MO;
        if (d == 0) {
          zero = true;
        } else {
          prod *= d;
          prod %= MO;
        }
      }
      debug {
        writeln("zero = ", zero, ", prod = ", prod);
      }
      
      long ans;
      foreach (i; 0 .. K + 2) {
        const d = (N - i) % MO;
        long tmp = f[i];
        if (zero) {
          tmp *= ((d == 0) ? prod : 0);
          tmp %= MO;
        } else {
          tmp *= prod;
          tmp %= MO;
          tmp *= modInv(d, MO);
          tmp %= MO;
        }
        tmp *= invFac[i];
        tmp %= MO;
        tmp *= invFac[K + 1 - i];
        tmp %= MO;
        tmp *= (((K + 1 - i) % 2 != 0) ? -1 : +1);
        tmp %= MO;
        ans += tmp;
        ans %= MO;
      }
      ans = (ans % MO + MO) % MO;
      writeln(ans);
    }
  } catch (EOFException e) {
  }
}
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