#include <bits/stdc++.h>
using namespace std;
#define REP(i,n) for(int i=0;i<(n);i++)

using ll=long long;
vector<pair<int,int>> P[37];
const ll MOD=100000009;

template<typename T,typename Comp>
using pque=priority_queue<T,vector<T>,Comp>;

pque<int,greater<>> que[3];

int solve(){
  ll s,n,k,b;cin>>s>>n>>k>>b;
  REP(_,n+1){
    //cerr<<s<<endl;
    ll cpy=s;
    REP(i,P[b].size()){
      int cnt=0;
      while(cpy%P[b][i].first==0){
        cnt++;
        cpy/=P[b][i].first;
      }
      //cerr<<P[b][i].first<<":"<<cnt<<endl;
      que[i].push(cnt);
    }
    s=1+ s*(s+12345)%MOD;
  }
  int res=1e9;
  REP(i,P[b].size()){
    int cnt=0;
    REP(_,k){
      cnt+=que[i].top();que[i].pop();
    }
    while(que[i].size())que[i].pop();
    //cerr<<cnt<<","<<P[b][i].first<<","<<P[b][i].second<<endl;
    res=min(res,cnt/P[b][i].second);
  }
  return res;
}

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

  for(int b=2;b<=36;b++){
    int now=b;
    for(int i=2;i<=36;i++){
      if(now%i)continue;
      int cnt=0;
      while(now%i==0){
        now/=i;
        cnt++;
      }
      P[b].emplace_back(i,cnt);
    }
  }
  for(int b=2;b<=36;b++){
    //cerr<<b<<":";for(const auto&[a,c]:P[b])cerr<<"["<<a<<","<<c<<"]";
    //cerr<<endl;
  }

  int testsize;cin>>testsize;
  while(testsize--)cout<<solve()<<'\n';
}