#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int MOD = 100000009;

vector<pair<int, int>> prime_factorize(int n) {
    vector<pair<int, int>> ret;
    for (int i = 2; i * i <= n; i++) {
        if (n % i == 0) {
            int num = 0;
            while (n % i == 0) {
                num++;
                n /= i;
            }
            ret.push_back({i, num});
        }
    }
    if (n != 1)
        ret.push_back({n, 1});
    return ret;
}

int main() {
    int Q;
    cin >> Q;
    while (Q--) {
        ll 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] + X[i - 1] * 12345) % MOD);
        }
        int ans = 1e9;
        auto pf = prime_factorize(B);
        for (auto& p : pf) {
            vector<int> cnt(N + 1);
            int prime = p.first;
            for (int i = 0; i <= N; i++) {
                int n = 0;
                int tmp = prime;
                while (X[i] && X[i] % tmp == 0) {
                    tmp *= prime;
                    n++;
                }
                cnt[i] = n;
            }
            sort(cnt.begin(), cnt.end());
            int sum = 0;
            for (int i = 0; i < K; i++) {
                sum += cnt[i];
            }
            ans = min(ans, sum / p.second);
        }
        cout << ans << endl;
    }
}