#include <bits/stdc++.h>
using namespace std;
long long mod=100000009;
long long primes[]={2,3,5,7,11,13,17,19,23,29,31};
void solve(){
	long long seed,N,B,K;
	scanf("%lld%lld%lld%lld",&seed,&N,&K,&B);
	long long X[N+1],p[N+1],ans=INT_MAX,count,elem[11];
	X[0]=seed;
	for(int i=0;i<11;++i){
		elem[i]=0;
		while(B%primes[i]==0){
			elem[i]+=1;
			B/=primes[i];
		}
	}
	for(int i=0;i<N;++i){
		X[i+1]=1+(X[i]*(X[i]+12345ll))%mod;
	}
	for(int i=0;i<11;++i){
		if(elem[i]==0){
			continue;
		}
		for(int j=0;j<N+1;++j){
			p[j]=0;
			long long temp=X[j];
			while(temp%primes[i]==0){
				temp/=primes[i];
				p[j]+=1;
			}
		}
		sort(p,p+N+1);
		count=0;
		for(int j=0;j<K;++j){
			count+=p[j];
		}
		ans=min(ans,count/elem[i]);
	}
	printf("%d\n",ans);
}
int main(){
	int T;
	scanf("%d",&T);
	for(int i=0;i<T;++i){
		solve();
	}
}