#include<bits/stdc++.h>
using namespace std;
using Int=long long;
using Real=long double;
template<class T,class S>inline bool chmin(T&A,S B){if(A>B){A=B;return true;}else{return false;}}
template<class T,class S>inline bool chmax(T&A,S B){if(A<B){A=B;return true;}else{return false;}}
#define REP(i,n)for(int i=0;i<(n);i++)
#define REP1(i,n)for(int i=0;i++<(n);)
#define ALL(x)begin(x),end(x)
#define drop(x){cout<<(x)<<'\n';return;}
int seed,N,K,B;
int cnt[40],A[10101];
Int X[10101];
void sol()
{
	REP(i,40)cnt[i]=0;
	cin>>seed>>N>>K>>B;
	X[0]=seed;
	REP1(i,N)X[i]=1+(X[i-1]*X[i-1]+X[i-1]*12345)%100000009;
	vector<int>pB;
	for(int i=2;i*i<=B;++i)
	{
		while(B%i==0)
		{
			B/=i;
			pB.push_back(i);
		}
	}
	if(B>1)pB.push_back(B);
	for(int p:pB)++cnt[p];
	pB.erase(unique(ALL(pB)),end(pB));
	int ans=1e9;
	for(int p:pB)
	{
		REP(i,N+1)
		{
			A[i]=0;
			while(X[i]%p==0)
			{
				X[i]/=p;
				++A[i];
			}
		}
		sort(A,A+N+1);
		chmin(ans,accumulate(A,A+K,0)/cnt[p]);
	}
	cout<<ans<<'\n';
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	cout<<fixed<<setprecision(16);
	int T=1;
	cin>>T;
	while(T--)sol();
}