#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi  = vector<int>; using vb  = vector<bool>; using vd  = vector<double>; using vl  = vector<ll>;
using vvi = vector<vi>;  using vvb = vector<vb>;   using vvd = vector<vd>;     using vvl = vector<vl>;

#define REP(i,n) for(ll i=0; i<(n); ++i)
#define FOR(i,b,n) for(ll i=(b); i<(n); ++i)
#define ALL(v) (v).begin(), (v).end()
#define TEN(x) ((ll)1e##x)
#define MOD 100000009

pair<vl, vl> primeFactors(ll n){
    vl p,e;
    ll m = n;
    for(ll i = 2; i*i <= n; i++){
        if(m%i != 0) continue;
        int c = 0;
        while(m%i == 0) c++, m /= i;
        p.push_back(i); e.push_back(c);
    }
    if(m > 1){
        p.push_back(m); e.push_back(1);
    }
    return make_pair(p,e);
}

int main() {
	// cin.tie(0);
	// ios_base::sync_with_stdio(false);
	cout << fixed << setprecision(5);
	ll q;
	cin >> q;

	REP(_, q) {
		ll seed, n, k, b;
		cin >> seed >> n >> k >> b;
		auto pfs = primeFactors(b);

		vl x(n + 1); x[0] = seed;
		FOR(i, 1, n + 1) x[i] = 1 + (x[i - 1] * x[i - 1] + x[i - 1] * 12345) % MOD;

		ll min_v = 100000;
		REP(i_pfs, pfs.first.size()) {
			vl x_factors(n + 1, 0);
			REP(i_x, n + 1) {
				ll v = x[i_x];
				while (v%pfs.first[i_pfs] == 0) {
					x_factors[i_x]++;
					v /= pfs.first[i_pfs];
				}
			}
			sort(ALL(x_factors));
			ll sum = 0; REP(i_x, k) sum += x_factors[i_x];
			min_v = min(min_v, sum / pfs.second[i_pfs]);
		}

		cout << min_v << endl;
	}

	return 0;
}