【BZOJ2142】礼物【扩展Lucas】

【题目链接】

原来那个板有问题...重新写了下。

把分解质因数写挂了，WA了一次...

/* Telekinetic Forest Guard */
#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long LL;

const int maxn = 10;

LL w[maxn];

inline LL mul(LL a, LL b, LL p) {
return (a * b - (LL)(a / (long double) p * b + 1e-6) * p + p) % p;
}

inline LL qpow(LL x, LL n, LL p) {
LL res = 1;
for(; n; n >>= 1, x = mul(x, x, p)) if(n & 1) res = mul(res, x, p);
return res;
}

inline void exgcd(LL a, LL b, LL &x, LL &y) {
b ? (exgcd(b, a % b, y, x), y -= a / b * x) : (x = 1, y = 0);
}

inline LL inv(LL a, LL p) {
LL x, y;
exgcd(a, p, x, y);
if(x < 0) x += p;
return x;
}

inline LL fact(LL n, LL pi, LL pk) {
if(n == 0 || n == 1) return 1;
LL res = 1;
for(LL i = 2; i <= n && i <= pk; i++) if(i % pi) res = mul(res, i, pk);
res = qpow(res, n / pk, pk);
for(LL k = n % pk, i = 2; i <= n && i <= k; i++) if(i % pi) res = mul(res, i, pk);
return mul(res, fact(n / pi, pi, pk), pk);
}

inline LL calc(LL n, LL m, LL p, LL pi, LL pk) {
LL a = fact(n, pi, pk), b = fact(m, pi, pk), c = fact(n - m, pi, pk), k = 0;
for(LL i = n / pi; i; i /= pi) k += i;
for(LL i = m / pi; i; i /= pi) k -= i;
for(LL i = (n - m) / pi; i; i /= pi) k -= i;
LL res = mul(mul(mul(a, inv(b, pk), pk), inv(c, pk), pk), qpow(pi, k, pk), pk);
return mul(mul(res, p / pk, p), inv(p / pk, pk), p);
}

int cnt, pr[100], pk[100];

inline LL C(LL n, LL m, LL p) {
LL ans = 0;
for(int i = 1; i <= cnt; i++)
(ans += calc(n, m, p, pr[i], pk[i])) %= p;
return ans;
}

inline void getpr(int p) {
for(int i = 2; p > 1; i++) if(p % i == 0) {
pr[++cnt] = i;
for(pk[cnt] = 1; p % i == 0; p /= i) pk[cnt] *= i;
}
}

int main() {
LL p, n, m;
scanf("%lld%lld%lld", &p, &n, &m);
LL sum = 0;
for(int i = 1; i <= m; i++) scanf("%lld", &w[i]), sum += w[i];

if(sum > n) {
printf("Impossible\n");
return 0;
}

getpr(p);

LL ans = 1;
for(int i = 1; i <= m; i++)
ans = mul(ans, C(n, w[i], p), p), n -= w[i];

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