#include <algorithm>
#include <iostream>
#include <utility>
#include <vector>

std::vector<std::pair<int, int>> prime_factorize(int n) {
    std::vector<std::pair<int, int>> res;
    std::vector<int> primes = {2, 3, 5, 7};
    for (int p : primes) {
        int e = 0;
        while (n % p == 0) {
            n /= p;
            e++;
        }
        if (e > 0) { res.emplace_back(p, e); }
    }
    if (n > 1) { res.emplace_back(n, 1); }
    return res;
}

void solve() {
    using namespace std;
    constexpr long long MOD = 100000009;
    long long seed;
    int n, k, base;
    cin >> seed >> n >> k >> base;
    vector<long long> x(n + 1, seed);
    for (int i = 0; i < n; i++) {
        x[i + 1] = (x[i] * (x[i] + 12345) % MOD) + 1;
    }
    auto primes = prime_factorize(base);
    int ans = n * 100;
    for (auto [p, e] : primes) {
        vector<int> count;
        for (auto xi : x) {
            int c = 0;
            while (xi % p == 0) {
                xi /= p;
                c++;
            }
            count.push_back(c);
        }
        sort(count.begin(), count.end());
        int mul_cnt = 0;
        for (int i = 0; i < k; i++) { mul_cnt += count[i]; }
        ans = min(ans, mul_cnt / e);
    }
    cout << ans << "\n";
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int q;
    std::cin >> q;
    while (q--) { solve(); }
}