#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long ll;

const int INF = 1 << 25;
const int MOD = 100000009;

vector<int> gen(int seed, int N){
	vector<int> x(N + 1);
	x[0] = seed;

	for(int n=1;n<=N;n++){
		ll pre = x[n-1];

		x[n] = 1 + (pre * pre % MOD + pre * 12345ll % MOD) % MOD;
	}

	return x;
}

vector< pair<int,int> > getFactors(int n){
	vector< pair<int,int> > res;
	for(int p=2;p*p<=n;p++)if(n % p == 0){
		int e = 0;
		while(n % p == 0){
			++e;
			n /= p;
		}
		res.push_back(make_pair(p, e));
	}
	if(n != 1){
		res.push_back(make_pair(n, 1));
	}

	return res;
}

int solve(int seed, int N, int K, int B){
	vector<int> x = gen(seed, N);
	vector< pair<int,int> > factors = getFactors(B);

	int res = INF;

	for(int i=0;i<factors.size();i++){
		int p = factors[i].first;
		int e = factors[i].second;

		vector<int> y = x;
		for(int j=0;j<y.size();j++){
			int num = y[j];
			int cnt = 0;

			while(num % p == 0){
				++cnt;
				num /= p;
			}

			y[j] = cnt;
		}

		sort(y.begin(), y.end());

		int sum = 0;
		for(int j=0;j<K;j++)sum += y[j];

		res = min(res, sum / e);
	}

	return res;
}

int main(){
	int Q;
	cin >> Q;
	for(int i=0;i<Q;i++){
		int seed, N, K, B;
		cin >> seed;
		cin >> N;
		cin >> K;
		cin >> B;
	
		cout << solve(seed, N, K, B) << endl;
	}
	return 0;
}