#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
#include <unordered_set>
#include <random>
#include <cassert>
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
const ll MOD=100000009;
vector<P> f[37];
int main()
{
	for(int i=2; i<=36; i++){
		int i1=i;
		for(int j=2; j<=31; j++){
			if(i1%j==0){
				int e=0;
				while(i1%j==0){
					i1/=j;
					e++;
				}
				f[i].push_back(P(j, e));
			}
		}
	}
	int q; cin>>q;
	for(int t=0; t<q; t++){
		ll s; cin>>s;
		int n, k, b; cin>>n>>k>>b;
		int ans=1e9;
		for(int j=0; j<f[b].size(); j++){
			ll p=f[b][j].first; int e=f[b][j].second;
			vector<int> v;
			ll x=s;
			for(int i=0; i<=n; i++){
				int e1=0;
				ll x1=x;
				while(x1%p==0){
					x1/=p;
					e1++;
				}
				v.push_back(e1);
				x=1+(x*x+x*12345)%MOD;
			}
			sort(v.begin(), v.end());
			int ct=0;
			for(int i=0; i<k; i++) ct+=v[i];
			ans=min(ans, ct/e);
		}
		cout<<ans<<endl;
	}
	return 0;
}