#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef pair<ll, ll> p_ll;

template<class T>
void debug(T itr1, T itr2) { auto now = itr1; while(now<itr2) { cout << *now << " "; now++; } cout << endl; }
#define repr(i,from,to) for (int i=(int)from; i<(int)to; i++)
#define all(vec) vec.begin(), vec.end()
#define rep(i,N) repr(i,0,N)
#define per(i,N) for (int i=(int)N-1; i>=0; i--)

const ll MOD = pow(10,8)+9;
const ll LLINF = pow(2,61)-1;
const int INF = pow(2,30)-1;

vector<ll> fac;
void c_fac(int x=pow(10,6)+10) { fac.resize(x,true); rep(i,x) fac[i] = i ? (fac[i-1]*i)%MOD : 1; }
ll inv(ll a, ll m=MOD) { ll b = m, x = 1, y = 0; while (b!=0) { int d = a/b; a -= b*d; swap(a,b); x -= y*d; swap(x,y); } return (x+m)%m; }
ll nck(ll n, ll k) { return fac[n]*inv(fac[k]*fac[n-k]%MOD)%MOD; }
ll gcd(ll a, ll b) { if (a<b) swap(a,b); return b==0 ? a : gcd(b, a%b); }
ll lcm(ll a, ll b) { return a/gcd(a,b)*b; }

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

vector<bool> isp;

void sieve(int x=pow(10,6)+10) {
  isp.resize(x,true); 
  isp[0] = false;
  isp[1] = false;
  for (int i=2; pow(i,2)<=x; i++) {
    if (isp[i]) for(int j=2; i*j<=x; j++) isp[i*j] = false;
  }
}

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

int main() {
  sieve();
  ll Q; cin >> Q;
  rep(_,Q) {
    ll seed, N, K, B; cin >> seed >> N >> K >> B;
    ll tb = B;
    vector<p_ll> p; 
    rep(i,B+1) {
      if (isp[i]&&tb%i==0) {
        ll count = 0; while (tb%i==0) { tb/=i; count++; }
        p.push_back(make_pair(i,count));
      }
    }
    // for (auto x: p) cout << x.first << "->" << x.second << " "; cout << endl;
    ll ps = p.size(), now = seed;
    ll num[ps][N+1] = {};
    rep(i,N+1) {
      if (i!=0) now = 1 + (now*now+now*12345) % MOD;
      ll tn = now;
      rep(j,ps) {
        while (tn%p[j].first==0) {
          tn /= p[j].first;
          num[j][i]++;
        }
      }
    }
    rep(i,ps) sort(num[i],num[i]+(N+1));
    // rep(i,ps) debug(num[i],num[i]+(N+1));
    ll result = LLINF;
    rep(i,ps) {
      ll count = 0; rep(j,K) count += num[i][j];
      count /= p[i].second;
      result = min(result, count);
    }
    cout << result << endl;
  }
  return 0;
}