逆元求组合数

题目链接

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define mod 998244353
#define maxn 500100
ll fac[maxn] = {0}, inv[maxn] = {0};
ll q_pow(ll a, ll b){
    ll ans = 1;
    while(b){
        if(b&1) ans = ans*a%mod;
        a = a*a%mod;
        b >>= 1;
    }
    return ans;
    
}
ll C(int n, int m){
    return fac[n]*inv[m]%mod*inv[n-m]%mod;
}
void init()
{
    fac[0] = 1;
    for(int i = 1; i < maxn; i++)
        fac[i] = fac[i-1] * i % mod;
    inv[maxn-1] = q_pow(fac[maxn-1], mod-2);
    for(int i = maxn-2; i >= 0; i--)
        inv[i] = inv[i+1]*(i+1)%mod;
}
int main()
{
    init();
    int n, k;
    cin >> n  >> k;
    ll ans = 0;
    for(int i = 1; i <= n; i++){
        if(n/i < k) break;
        ans = (ans + C(n/i-1, k-1) % mod) % mod;
    }
    printf("%lld
", ans);
    
}