#include <cstdio>
#include <iostream>
#include <sstream>
#include <fstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <limits>
#include <climits>
#include <cfloat>
#include <functional>
using namespace std;

void integerFactorization(int n, vector<int>& base, vector<int>& expo)
{
    base.clear();
    expo.clear();
    int a = 2;
    while(a * a <= n){
        int b = 0;
        while(n % a == 0){
            ++ b;
            n /= a;
        }
        if(b > 0){
            base.push_back(a);
            expo.push_back(b);
        }
        ++ a;
    }
    if(n > 1){
        base.push_back(n);
        expo.push_back(1);
    }
}

int solve(vector<int> x, int k, int b)
{
    int n = x.size();

    vector<int> base, expo;
    integerFactorization(b, base, expo);

    int ret = INT_MAX;
    for(unsigned i=0; i<base.size(); ++i){
        vector<int> v(n, 0);
        for(int j=0; j<n; ++j){
            while(x[j] % base[i] == 0){
                ++ v[j];
                x[j] /= base[i];
            }
        }
        sort(v.begin(), v.end());
        ret = min(ret, accumulate(v.begin(), v.begin() + k, 0) / expo[i]);
    }
    return ret;
}

int main()
{
    int q;
    cin >> q;

    while(--q >= 0){
        int seed, n, k, b;
        cin >> seed >> n >> k >> b;

        vector<int> x(n+1);
        x[0] = seed;
        for(int i=1; i<=n; ++i)
            x[i] = 1 + x[i-1] * (x[i-1] + 12345LL) % 100000009;

        cout << solve(x, k, b) << endl;
    }

    return 0;
}