NOIp2011 计算系数

组合数学

Luogu

通过二项式定理可知答案为 $\tbinom{k}{n} \cdot a^n b^m$。

那么直接计算就行了。

#include <iostream>
#include <cstdio>
typedef long long LL;
#define int LL
const int MOD = 10007;
int a, b, k, n, m;
inline int read() {
    register int x = 0;
    register char ch = getchar();
    while(!isdigit(ch)) ch = getchar();
    while(isdigit(ch)) {
        x = x * 10 + ch - '0';
        ch = getchar();
    }
    return x;
}
inline int fPow(int x, int y) {
    int res = 1, base = x;
    while(y) {
        if(y & 1) res = res * base % MOD;
        base = base * base % MOD;
        y >>= 1;
    }
    return res;
}
inline int C(int x, int y) {
    int xx = 1, yy = 1;
    for(int i = y + 1; i <= x; ++i) xx = xx * i % MOD;
    for(int i = 1; i <= x - y; ++i) yy = yy * i % MOD;
    return xx * fPow(yy, MOD - 2) % MOD;
}
signed main() {
    a = read();
    b = read();
    k = read();
    n = read();
    m = read();
    printf("%lld\n", C(k, n) * fPow(a, n) * fPow(b, m) % MOD);
    return 0;
}