比赛 寒假集训2 评测结果 WWWMMMMMMMMMMMMMMMMM
题目名称 组合数问题 最终得分 0
用户昵称 LikableP 运行时间 2.485 s
代码语言 C++ 内存使用 1.47 MiB
提交时间 2026-02-25 10:08:18
显示代码纯文本
#include <cstdio>
typedef long long ll;

ll EXGCD(ll a, ll b, ll &x, ll &y) {
  if (b == 0) {
    x = 1, y = 0;
    return a;
  }
  ll d = EXGCD(b, a % b, x, y);
  ll z = x;
  x = y;
  y = z - (a / b) * y;
  return d;
}

ll inverse(ll a, ll mod) {
  ll x, y;
  EXGCD(a, mod, x, y);
  return (x % mod + mod) % mod;
}

ll n, x, p, m;
ll a[1010];

ll f(ll k) {
  ll res = 0, kk = 1;
  for (int i = 0; i <= m; ++i) {
    res = (res + a[i] * kk) % p;
    kk = kk * k % p;
  }
  return res;
}

ll frac[1010], inv[1010];

ll C(ll x, ll y) {
  return frac[x] * inv[y] % p * inv[x - y] % p;
}

int main() {
  #ifdef LOCAL
    freopen("!input.in", "r", stdin);
    freopen("!output.out", "w", stdout);
  #else
    freopen("problem.in", "r", stdin);
    freopen("problem.out", "w", stdout);
  #endif

  scanf("%lld %lld %lld %lld", &n, &x, &p, &m);
  for (int i = 0; i <= m; ++i) {
    scanf("%lld", &a[i]);
    a[i] %= p;
  }

  frac[0] = inv[0] = 1;
  for (int i = 1; i <= 1000; ++i) {
    frac[i] = frac[i - 1] * i % p;
    inv[i] = inverse(frac[i], p);
  }

  ll ans = 0, xx = 1;
  for (ll k = 0; k <= n; ++k) {
    ans = (ans + f(k) * xx % p * C(n, k) % p) % p;
    xx = xx * x % p;
  }

  printf("%lld\n", ans);
  return 0;
}