#include <stdio.h>
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace atcoder;
using mint = modint998244353;
using namespace std;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define Inf 100000001

int main(){
	
	int Q;
	cin>>Q;
	
	rep(_,Q){
		long long seed,N,K,B;
		cin>>seed>>N>>K>>B;
		vector<pair<int,int>> ps;
		
		for(int i=2;i<=B;i++){
			if(B%i==0){
				ps.emplace_back(i,0);
				while(B%i==0){
					B/=i;
					ps.back().second++;
				}
			}
		}
		
		vector<long long> a(N+1);
		a[0] = seed;
		for(int i=1;i<=N;i++){
			a[i] = a[i-1] * (a[i-1] + 12345);
			a[i] %= 100000009;
			a[i]++;			
		}
		
		int ans = Inf;
		rep(i,ps.size()){
			vector<int> cnt(35,0);
			rep(j,N+1){
				int temp = a[j];
				int c = 0;
				while(temp%ps[i].first==0){
					temp /= ps[i].first;
					c++;
				}
				cnt[c]++;
			}
			int KK = K;
			int S = 0LL;
			rep(j,cnt.size()){
				if(KK<=cnt[j]){
					S += j * KK;
					break;
				}
				
				KK -= cnt[j];
				S += cnt[j] * j;
			}
			ans = min(ans,S/ps[i].second);
		}
		cout<<ans<<endl;
		
	}
	
	return 0;
}