#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}


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

//INSERT ABOVE HERE
const Int MOD = 100000009;
signed main(){
  Int T;
  cin>>T;
  while(T--){
    Int s,n,k,b;
    cin>>s>>n>>k>>b;
    vector<Int> x(n+1,s);
    for(Int i=1;i<=n;i++) x[i]=1+(x[i-1]*x[i-1]+x[i-1]*12345)%MOD;
    for(Int i=0;i<=n;i++){
      if(x[i]==0){
        cout<<0<<endl;
        continue;
      }
    }
    Int ans=1e9;
    auto m=factorize(b);
    for(auto p:m){
      vector<Int> cnt(40);
      for(Int i=0;i<=n;i++){
        Int k=x[i],c=0;
        while(k%p.first==0){
          k/=p.first;
          c++;
        }
        cnt[c]++;
      }
      Int res=0,num=0;
      for(Int i=0;i<(Int)cnt.size();i++){
        Int d=min(k-num,cnt[i]);
        num+=d;
        res+=d*i;
      }     
      chmin(ans,res/p.second);
    }
    cout<<ans<<endl;
  }
  return 0;
}