// includes
#include <cassert>
#include <cstdio>
#include <cstdint>
#include <cstring>
#include <iostream>
#include <iomanip>
#include <string>
#include <queue>
#include <stack>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <algorithm>
#include <utility>
#include <functional>
#include <cmath>
#include <climits>
#include <bitset>
#include <list>
#include <random>

// macros
#define ll long long int
#define pb emplace_back
#define mk make_pair
#define pq priority_queue
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define rep(i, n) FOR(i, 0, n)
#define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end())

using namespace std;

//  types
typedef pair<int, int> P;
typedef pair<ll, int> Pl;
typedef pair<ll, ll> Pll;
typedef pair<double, double> Pd;
 
// constants
const int inf = 1e9;
const ll linf = 1LL << 50;
const double EPS = 1e-10;
const int mod = 100000009;

// solve
template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;}
template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;}

template <typename T>
map<T, int> factorize(T n){
  map<T, int> res;
  T tmp = n;
  for(T i = 2; i * i <= n; i++){
    while(tmp % i == 0){
      ++res[i];
      tmp /= i;
    }
  }
  if(tmp != 1)res[tmp] = 1;
  return res;
}

ll next(ll x){
  return 1 + (x * x % mod + x * 12345 % mod) % mod;
}

int main(int argc, char const* argv[])
{
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int q;
  cin >> q;
  rep(i_, q){
    ll x;
    int n, k, b;
    cin >> x >> n >> k >> b;
    auto f = factorize(b);
    map<int, vector<int> > mp;
    rep(i, n + 1){
      for(auto itr = f.begin(); itr != f.end(); ++itr){
        int key = itr->first;
        ll tmp = x;
        int cnt = 0;
        while(tmp % key == 0){
          tmp /= key;
          cnt++;
        }
        mp[key].pb(cnt);
      }
      x = next(x);
    }
    int res = inf;
    for(auto itr = f.begin(); itr != f.end(); ++itr){
      int key = itr->first;
      int p = itr->second;
      vector<int> v = mp[key];
      sort(all(v));
      int cnt = 0;
      rep(j, k)cnt += v[j];
      res = min(res, cnt / p);
    }
    cout << res << endl;
  }
	return 0;
}