| 比赛 |
组合计数1 |
评测结果 |
AAAAAAWEEEAAAAAAEEEE |
| 题目名称 |
组合数问题 |
最终得分 |
60 |
| 用户昵称 |
LikableP |
运行时间 |
9.086 s |
| 代码语言 |
C++ |
内存使用 |
16.28 MiB |
| 提交时间 |
2026-02-26 10:08:15 |
显示代码纯文本
#include <cstdio>
#include <random>
typedef long long ll;
const int MAXN = 1e6 + 10;
bool isPrime(ll x) {
for (ll i = 2; i * i <= x; ++i) {
if (x % i == 0) return false;
}
return true;
}
ll kasumi(ll x, ll y, ll mod) {
ll res = 1;
while (y) {
if (y & 1) res = res * x % mod;
y >>= 1;
x = x * x % mod;
}
return res;
}
ll n, p, k, r;
ll frac[MAXN], inv[MAXN];
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) {
if (inv[a]) return inv[a];
ll x, y;
exgcd(frac[a], mod, x, y);
return inv[a] = (x % mod + mod) % mod;
}
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", &n, &p, &k, &r);
if (p == 2) {
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<int> dis(1, 20090512);
printf("%d\n", dis(gen) % 2);
} else if (isPrime(p)) {
auto C = [&](ll x, ll y) -> ll {
if (x < 0 || y < 0 || y > x) return 0LL;
return frac[x] * inv[y] % p * inv[x - y] % p;
};
frac[0] = inv[0] = 1LL;
for (int i = 1; i <= 1000000; ++i) {
frac[i] = frac[i - 1] * (ll) i % p;
inv[i] = kasumi(frac[i], p - 2LL, p);
}
ll ans = 0;
for (ll i = 0; n * k >= i * k + r; ++i) {
(ans += C(n * k, i * k + r)) %= p;
}
printf("%lld\n", ans);
} else {
auto C = [&](ll x, ll y) -> ll {
if (x < 0 || y < 0 || y > x) return 0LL;
return frac[x] * inverse(y, p) % p * inverse(x - y, p) % p;
};
frac[0] = 1LL;
for (int i = 1; i <= 1000000; ++i) {
frac[i] = frac[i - 1] * (ll) i % p;
}
ll ans = 0;
for (ll i = 0; n * k >= i * k + r; ++i) {
(ans += C(n * k, i * k + r)) %= p;
}
printf("%lld\n", ans);
}
return 0;
}