#include <iostream>
#include <cstdint>
#include <climits>
#include <algorithm>
#include <vector>
#include <map>

using namespace std;

typedef int64_t ll;

void calc()
{
	int seed, N, K, B;
	cin >> seed >> N >> K >> B;
	map<int,int> prime;

	int b = B;
	for (int i = 2; i <= B && b > 1; i++) {
		while ((b % i) == 0) {
			prime[i]++;
			b /= i;
		}
	}

	vector<ll> X(N + 1);
	X[0] = seed;
	for (int i = 1; i <= N; i++) {
		X[i] = 1 + (X[i - 1] * X[i - 1] + X[i - 1] * 12345) % ll(100000009);
	}

	int result = INT_MAX;
	vector<int> Y(N + 1);
	for (auto pr : prime) {
		for (int i = 0; i <= N; i++) {
			ll x = X[i];
			Y[i] = 0;
			while ((x % pr.first) == 0) {
				Y[i]++;
				x /= pr.first;
			}
		}
		sort(Y.begin(), Y.end());
		int res = 0;
		for (int i = 0; i < K; i++) {
			res += Y[i];
		}
		result = min(result, res / pr.second);
	}
	cout << result << endl;
}

int main()
{
	int Q;
	cin >> Q;
	for (int q = 0; q < Q; q++) {
		calc();
	}
}