#include <bits/stdc++.h>
using namespace std;

using ll = long long;
constexpr int mod = 1e8 + 9;

int solve(void) {
	int seed, N, K, B;
	cin >> seed >> N >> K >> B;
	
	vector<ll> X(N + 1);
	X[0] = seed;
	for(int i = 1; i <= N; ++i) X[i] = 1 + (X[i - 1] * X[i - 1] % mod + X[i - 1] * 12345 % mod) % mod;
	
	auto solve = [&](int p) ->int {
		vector<int> Y(N + 1, 0);
		for(int i = 0; i <= N; ++i) while(X[i] % p == 0) X[i] /= p, ++Y[i];
		sort(Y.begin(), Y.end());
		
		int res = 0;
		for(int i = 0; i < K; ++i) res += Y[i];
		return res;
	};
	
	int ans = 1e9;
	for(int i = 2; i <= B; ++i) {
		int cnt = 0;
		while(B % i == 0) B /= i, ++cnt;
		if(cnt) ans = min(ans, solve(i) / cnt);
	}
	
	cout << ans << endl;
	return 0;
}

int main(void) {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);
	
	int Q;
	cin >> Q;
	
	while(Q--) solve();
	
	return 0;
}