Codeforces 439E Devu and Birthday Celebration 容斥

我们发现不合法的整除因子在 m 的因子里面，然后枚举m的因子暴力容斥，或者用莫比乌斯系数容斥。
#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define fio ios::sync_with_stdio(false); cin.tie(0);

using namespace std;

const int N = 1e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

template<class T, class S> inline void add(T& a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T& a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T& a, S b) {return a < b ? a = b, true : false;}
template<class T, class S> inline bool chkmin(T& a, S b) {return a > b ? a = b, true : false;}

int miu[N];
vector<int> fac[N];
int cnt[N], n, m;

int F[N], Finv[N], inv[N];
int C(int n, int m) {
    if(n < 0 || n < m) return 0;
    return 1LL * F[n] * Finv[m] % mod * Finv[n - m] % mod;
}

inline int calc(int n, int m) {
    if(m < n) return 0;
    return C(m - 1, n - 1);
}

int main() {
    inv[1] = F[0] = Finv[0] = 1, miu[1] = 1;
    for(int i = 1; i < N; i++)
        for(int j = i + i; j < N; j += i)
            miu[j] -= miu[i];
    for(int i = 2; i < N; i++) inv[i] = 1LL * (mod - mod / i) * inv[mod % i] % mod;
    for(int i = 1; i < N; i++) F[i] = 1LL * F[i - 1] * i % mod;
    for(int i = 1; i < N; i++) Finv[i] = 1LL * Finv[i - 1] * inv[i] % mod;
    for(int i = 1; i < N; i++)
        for(int j = i; j < N; j += i)
            fac[j].push_back(i);
    int T; scanf("%d", &T);
    while(T--) {
        scanf("%d%d", &m, &n);
        int ans = 0;
        for(int i = 0; i < SZ(fac[m]); i++)
            ans = (ans + 1LL * miu[fac[m][i]] * calc(n, m / fac[m][i]) % mod + mod) % mod;
        printf("%d
", ans);
    }
    return 0;
}

/*
*/