CROC 2016 - Elimination Round (Rated Unofficial Edition) F - Cowslip Collections 数论 + 容斥

F - Cowslip Collections

http://codeforces.com/blog/entry/43868 这个题解讲的很好。。。

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define PII pair<int, int>
#define PLI pair<LL, int>
#define ull unsigned long long
using namespace std;
 
const int N = 1e6 + ;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + ;
const double eps = 1e-;
 
LL inv[N], f[N], finv[N], phi[N];
int n, k, q, a[N], in[N], cnt[N];
vector<int> fac[N];
 
void init() {
    inv[] = f[] = finv[] = ;
    for(int i = ; i < N; i++) inv[i] = (mod-mod/i)*inv[mod%i]%mod;
    for(int i = ; i < N; i++) f[i] = f[i-]*i%mod;
    for(int i = ; i < N; i++) finv[i] = finv[i-]*inv[i]%mod;
    iota(phi, phi + N, );
    for(int i = ; i < N; i++) {
        for(int j = i; j < N; j += i) {
            if(i != j) phi[j] -= phi[i];
            if(in[j]) fac[j].push_back(i);
        }
    }
}
LL comb(int n, int m) {
    if(n < m || n < ) return ;
    return f[n]*finv[n-m]%mod*finv[m]%mod;
}
int main() {
    scanf("%d%d%d", &n, &k, &q);
    for(int i = ; i <= n + q; i++) scanf("%d", &a[i]), in[a[i]] = ;
    init();
    LL ans = ;
    for(int i = ; i <= n + q; i++) {
        for(int t : fac[a[i]]) {
            ans = (ans + phi[t]*((comb(cnt[t]+, k)-comb(cnt[t], k)+mod)%mod)%mod)%mod;
            cnt[t]++;
        }
        if(i > n) printf("%lld\n", ans);
    }
    return ;
}
 
/*
*/