#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
typedef long long int ll;
typedef long double ld;
#define FOR(i,l,r) for(ll i=l;i<r;i++)
#define REP(i,n) FOR(i,0,n)
#define RFOR(i,l,r) for(ll i=r-1;i>=l;i--)
#define RREP(i,n) RFOR(i,0,n)
#define ALL(x) x.begin(),x.end()
#define P pair<ll,ll>
#define F first
#define S second
#define BS(A,x) binary_search(ALL(A),x)
#define LB(A,x) (ll)(lower_bound(ALL(A),x)-A.begin())
#define UB(A,x) (ll)(upper_bound(ALL(A),x)-A.begin())
#define COU(A,x) UB(A,x)-LB(A,x)
template<typename T>using min_priority_queue=priority_queue<T,vector<T>,greater<T>>;
using mint=modint1000000007;
signed main(){
  ll Q,mod=100000009;cin>>Q;
  REP(q,Q){
    ll seed,N,K,B,ans=1e18;cin>>seed>>N>>K>>B;vector<ll>X(N+1);X[0]=seed;
    REP(i,N)X[i+1]=1+(X[i]*X[i]+12345*X[i])%mod;vector<P>A;ll d=2;
    while(d*d<=B){if(B%d==0){ll t=0;while(B%d==0){B/=d;t++;}A.push_back(P(d,t));}d++;}
    if(B>1)A.push_back(P(B,1));
    REP(i,A.size()){
      vector<ll>Y(X);REP(j,N+1){ll t=0;while(Y[j]%A[i].F==0){Y[j]/=A[i].F;t++;}Y[j]=t;}
      sort(ALL(Y));ll res=0;REP(i,K)res+=Y[i];ans=min(ans,res/A[i].S);
    }
    cout<<ans<<endl;
  }
  return 0;
}