hdu6363 bookshelf 容斥+数列+数论gcd定理（也可以Möbius）

 

 

#define _CRT_SECURE_NO_WARNINGS
#include<cmath>
#include<iostream>
#include<stdio.h>
#include<algorithm>
#include<cstring>
using namespace std;
#define rep(i,t,n)  for(int i =(t);i<=(n);++i)
#define per(i,n,t)  for(int i =(n);i>=(t);--i)
#define mmm(a,b) memset(a,b,sizeof(a))
typedef long long ll;
const int maxn = 2e6 + 10;
const ll mod = 1e9 + 7;


int n, m, k;



ll inv[maxn], f[maxn], fac[maxn];
ll c[maxn];
long long kpow(long long a, long long n) {
    long long res = 1;
    while (n > 0) {
        if (n & 1)res = res * a%mod;
        a = a * a%mod;
        n >>= 1;
    }
    return res;
}
void init() {
    f[0] = 1; f[1] = 2;
    fac[0] = fac[1] = 1;
    inv[1] = 1;
    rep(i, 2, maxn) {
        fac[i] = fac[i - 1] * (ll)i % mod;
        inv[i] = kpow(fac[i], mod - 2);
        f[i] = (f[i - 1] * f[i - 2]) % mod;
        //f[i]-1==F[i]==2^fi-1
    }
}
ll C(int n, int m) {
    if (n < m) return 0ll;
    if (m == 0 || n == m) return 1ll;
    if (n - 1 == m || m == 1) return n;
    return fac[n] * inv[m] % mod * inv[n - m] % mod;
}

int main() {
    int t;
    cin >> t;
    init();
    while (t--) {
        cin >> n >> k;
        mmm(c, 0);ll ans = 0;
        per(g, n, 1) if(n%g==0){
            c[g] = C(n / g + k - 1, k - 1);    
            for (int gg = 2 * g; gg <= n; gg += g) {c[g] -= c[gg];if (c[g] < 0)c[g] += mod;}
            ans += c[g] * (f[g] - 1) % mod;ans %= mod;
        }
        ans *= kpow(C(n + k - 1, k - 1), mod - 2);ans %= mod;
        cout << ans << endl;
    }
}
/*



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