//#include <bits/stdc++.h>
#include <assert.h>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
#include <iterator>
using namespace std;

typedef signed long long ll;

#define pp(...) (void)printf(__VA_ARGS__)
#define For(x,to) for(x=0;x<(to);x++)
#define ForAuto(x,arr) for(auto& x:arr)
#define ForBeginEnd(x,c) for(__typeof(c.begin()) x=c.begin();x!=c.end();x++)
#define All(a) (a.begin()),(a.end())
#define Zeros(a) memset(a,0,sizeof(a))
#define Minus(a) memset(a,0xff,sizeof(a))

#define PI 3.14159265
#define EPS (1e-10)
#define EPS_eq(a,b) (abs((a)-(b)) < EPS)

#pragma GCC diagnostic ignored "-Wconversion"

//#define int long long
#define INF 1000*1000

int dxy[] = {0, 1, 0, -1, 0};

typedef pair<int, int> P;

void pp_int(int x){ printf("%d\n", x); };

int i,j,k;

ll M = 100000009;

//-------------------------------------------------

void init() {
    ios::sync_with_stdio(false);
}

map<ll, ll> fact(ll n){
    map<ll, ll> mp_fact;
    ll a = 2;
    while (n > 1) {
        while (n % a == 0) {
            mp_fact[a]++;
            n /= a;
        }
        a++;
    }
    return mp_fact;
}

signed main() { init();
    int q;cin>>q;
    while(q--){
        ll seed, N,K,B;
        vector<ll> xn;
        cin>>seed>>N>>K>>B;
        auto mp_fact = fact(B);
        xn.push_back(seed);
        map<int, vector<ll> > mp_set;
        For(i, N){
            ll prev = xn.back();
            ll next = 1 + (prev * prev + prev * 12345) % M;
            xn.push_back(next);
        }
        For(i, xn.size()){
            for(auto it : mp_fact) {
                ll factor = it.first;
                ll cnt = 0;
                ll t = xn[i];
                while(t % factor == 0) {
                    t /= factor;
                    cnt++;
                }
                mp_set[factor].push_back(cnt);
            }
        }

        ll mn = INF;

//        printf("seed: %lld\n", seed);
//
//        for(auto it : mp_fact){
//            printf("mp_fact[%lld] = %lld\n", it.first, it.second);
//        }
//
//        For(i, xn.size()){
//            printf("xn[%d] = %lld\n", i, xn[i]);
//        }

        for(auto it : mp_set) {
//            printf("mp_set_first: %d\n", it.first);
            sort(it.second.begin(), it.second.end());
            ll cnt = 0;
            for(i = 0; i < K; i++){
                cnt += it.second[i];
            }
            ll factor = it.first;
            mn = min(mn, cnt / mp_fact[factor]);
        }
        printf("%lld\n", mn);
    }

    return 0;
}