#include<cstdio>
#include<vector>
#include<algorithm>


using namespace std;
using ll=long long;
using ui=unsigned;

const ll MOD=100000009;


int calc(ll x, int b)
{
	int i;

	for(i=0;x%b==0;i++) x/=b;
	return i;
}


int min(int a, int b)
{
	if(a<b) return a;
	return b;
}


int min_u(int &m, int v)
{
	if(m>v)
	{
		m=v;
		return 1;
	}
	return 0;
}


int solve(int seed, int n, int k, int b)
{
	vector<ll> x(n+1);
	vector<int> e, en;
	vector<int> c(n+1);
	int ret=99999;

	for(int i=2;i<=b;i++)
	{
		int j;
		for(j=0;b%i==0;j++)
		{
			b/=i;
		}
		if(j)
		{
			e.push_back(i);
			en.push_back(j);
		}
	}

	x[0]=seed;
	for(int i=1;i<=n;i++)
	{
		x[i]=1+(x[i-1]*x[i-1]+x[i-1]*12345)%MOD;
	}

	for(ui j=0;j<e.size();j++)
	{
		int sum;
		for(int i=0;i<=n;i++)
		{
			c[i]=calc(x[i], e[j]);
		}
		sort(c.begin(), c.end());
		sum=0;
		for(int i=0;i<k;i++)
		{
			sum+=c[i];
		}
		min_u(ret, sum/en[j]);
	}

	return ret;
}


int main(void)
{
	int i, q, seed, n, k, b;

	while(scanf("%d", &q)==1)
	{
		for(i=0;i<q;i++)
		{
			scanf("%d%d%d%d", &seed, &n, &k, &b);
			printf("%d\n", solve(seed, n, k, b));
		}
	}

	return 0;
}