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

int main() {
  ios::sync_with_stdio(false);

  int Q;
  cin >> Q;

  while (Q--) {
    int Seed, N, K, B;
    cin >> Seed >> N >> K >> B;
    vector<int> X(N + 1); { 
      X[0] = Seed;
      for (int i = 1; i <= N; ++i) {
        X[i] = (1 + ((int64_t) X[i - 1] * X[i - 1] + (int64_t) X[i - 1] * 12345)) % 100000009;
      }
    }
    vector<pair<int, int>> pe; {
      int b = B;
      for (int i = 2; i * i <= b; ++i) {
        if (b % i == 0) {
          pe.emplace_back(0, i);
          while (b % i == 0) pe.back().first++, b /= i;
        }
      }
      if (b > 1) pe.emplace_back(1, b);
    }
    int res = 1 << 30;
    for (auto b : pe) {
      int q = b.second;
      function<int(int, int)> dcnt = [&](int v, int p) { return v % p ? 0 : 1 + dcnt(v / p, p); };
      sort(X.begin(), X.end(), [&](int a, int b) { return dcnt(a, q) < dcnt(b, q); });
      for (auto c : pe) {
        int r = 0;
        for (int i = 0; i < K; ++i) {
          r += dcnt(X[i], c.second);
        }
        res = min(res, r / c.first);
      }
    }
    cout << res << endl;
  }

  return 0;
}