#include <iostream>
#include <vector>
#include <queue>

template <class T>
using MinHeap = std::priority_queue<T, std::vector<T>, std::greater<T>>;

struct Prime {
    int max_n;
    std::vector<int> primes;
    std::vector<bool> isp;

    explicit Prime(int max_n)
        : max_n(max_n), isp(max_n + 1, true) {
        isp[0] = isp[1] = false;
        for (int i = 2; i * i <= max_n; ++i) {
            if (isp[i]) {
                for (int j = i; i * j <= max_n; ++j) {
                    isp[i * j] = false;
                }
            }
        }

        for (int p = 2; p <= max_n; ++p) {
            if (isp[p]) primes.push_back(p);
        }
    }

    template <class T>
    bool isprime(T n) const {
        if (n <= max_n) return isp[n];
        for (T p : primes) {
            if (p * p > n) break;
            if (n % p == 0) return false;
        }
        return true;
    }

    template <class T>
    std::vector<std::pair<T, int>> factorize(T n) const {
        std::vector<std::pair<T, int>> facts;
        for (T p : primes) {
            if (p * p > n) break;
            if (n % p != 0) continue;
            int exp = 0;
            while (n % p == 0) {
                n /= p;
                ++exp;
            }
            facts.emplace_back(p, exp);
        }
        if (n > 1) {
            facts.emplace_back(n, 1);
        }
        return facts;
    }

    template <class T>
    static std::vector<T> divisors(T n) {
        std::vector<T> ret;
        for (T p = 1; p * p <= n; ++p) {
            if (n % p != 0) continue;
            ret.push_back(p);
            if (n / p == p) continue;
            ret.push_back(n / p);
        }
        return ret;
    }
};

const Prime P(100);

using lint = long long;

constexpr int INF = 1 << 30;

lint next(lint x) {
    return (x * x + x * 12345) % 100000009 + 1;
}

lint dig(lint x, int b) {
    int ret = 0;
    while (x % b == 0) {
        x /= b;
        ++ret;
    }
    return ret;
}

void solve() {
    lint x;
    int n, k, b;
    std::cin >> x >> n >> k >> b;
    ++n;

    auto fs = P.factorize(b);
    int m = fs.size();

    std::vector<MinHeap<int>> heaps(m);
    while (n--) {
        for (int i = 0; i < m; ++i) {
            heaps[i].push(dig(x, fs[i].first));
        }
        x = next(x);
    }

    int ans = INF;
    for (int i = 0; i < m; ++i) {
        int sum = 0;

        for (int j = 0; j < k; ++j) {
            sum += heaps[i].top();
            heaps[i].pop();
        }

        ans = std::min(ans, sum / fs[i].second);
    }

    std::cout << ans << "\n";
}

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    int q;
    std::cin >> q;
    while (q--) solve();

    return 0;
}