题目

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
using namespace std;

const int maxn = 1e6+10;

typedef long long LL;

int p[maxn],cnt;
bool prime[maxn];
int fac[1000],tot;
int Count[1000];
LL sum[maxn];
void isprime(){
    memset(prime,0,sizeof(prime));
    cnt=0;
    for(int i=2;i<maxn;i++){
        if(!prime[i]){
            p[cnt++]=i;
            for(int j=i+i;j<maxn;j+=i) prime[j]=1;
        }
    }
}

void fenjie(int x){
    tot=0;
    memset(Count,0,sizeof(Count));
    for(int i=0;i<cnt&&p[i]*p[i]<=x;i++){
        if(x%p[i]==0){
            fac[tot]=p[i];
            while(x%p[i]==0) Count[tot]++,x/=p[i];
            tot++;
        }
    }
    if(x>1) fac[tot]=x,Count[tot++]=1;
}

LL getNum(int n,int p){
    if(n<p) return 0;
    return getNum(n/p,p)+(LL)n/p;
}

int main()
{
    isprime();
    int t,n,m,k;
    scanf("%d",&t);
    while(t--){
        scanf("%d%d%d",&n,&m,&k);
        fenjie(k);
        LL ans = 1000000000;
        for(int i=0;i<tot;i++){
            sum[i]=getNum(n,fac[i])-getNum(n-m,fac[i]);
            ans=min(sum[i]/Count[i],ans);
        }
        printf("%lld\n",ans);
    }
    return 0;
}