#include <bits/stdc++.h>
using namespace std;
const int INF = 1000000;
int main(){
  int Q;
  cin >> Q;
  for (int i = 0; i < Q; i++){
    int seed, N, K, B;
    cin >> seed >> N >> K >> B;
    vector<int> X(N + 1);
    X[0] = seed;
    for (int j = 0; j < N; j++){
      X[j + 1] = 1 + ((long long) X[j] * X[j] + (long long) X[j] * 12345) % 100000009;
    }
    vector<pair<int, int>> F;
    for (int j = 2; j <= B; j++){
      if (B % j == 0){
        int cnt = 0;
        while (B % j == 0){
          B /= j;
          cnt++;
        }
        F.push_back(make_pair(j, cnt));
      }
    }
    int cnt = F.size();
    int ans = INF;
    for (int j = 0; j < cnt; j++){
      int p = F[j].first;
      vector<int> Y(N + 1, 0);
      for (int k = 0; k <= N; k++){
        int x = X[k];
        while (x % p == 0){
          x /= p;
          Y[k]++;
        }
      }
      sort(Y.begin(), Y.end());
      int sum = 0;
      for (int k = 0; k < K; k++){
        sum += Y[k];
      }
      ans = min(ans, sum / F[j].second);
    }
    cout << ans << endl;
  }
}