| 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;
}