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


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

const ll MOD=100000009;


struct en_t
{
	int c[3];
	en_t operator+(const en_t& rhs)
	{
		return (en_t){c[0]+rhs.c[0], c[1]+rhs.c[1], c[2]+rhs.c[2]};
	}
	int cmp(const en_t& rhs)
	{
		if(c[0]==rhs.c[0] && c[1]==rhs.c[1] && c[2]==rhs.c[2]) return  0;
		if(c[0]<=rhs.c[0] && c[1]<=rhs.c[1] && c[2]<=rhs.c[2]) return -1;
		if(c[0]>=rhs.c[0] && c[1]>=rhs.c[1] && c[2]>=rhs.c[2]) return  1;
		return 2;
	}
};


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<en_t> c(n+1);
	vector<int> e, rm;
	vector<vector<en_t> > dp;
	en_t en={{0,0,0}}, tc;
	int t, is_need_add, ret=999999;

	dp.resize(k+1);
	dp[0].push_back(en);
	t=b;
	for(int i=2;i<=t;i++)
	{
		int j;
		for(j=0;t%i==0;j++)
		{
			t/=i;
		}
		if(j)
		{
			en.c[e.size()]=j;
			e.push_back(i);
		}
	}

	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(int i=0;i<=n;i++)
	{
		for(ui j=0;j<e.size();j++)
		{
			int k;
			for(k=0;x[i]%e[j]==0;k++)
			{
				x[i]/=e[j];
			}
			c[i].c[j]=k;
		}
	}

	for(int i=0;i<=n;i++)
	{
		for(int j=min(k-1, i);j>=0;j--)
		{
			for(ui k=0;k<dp[j].size();k++)
			{
				tc=dp[j][k]+c[i];
				is_need_add=1;
				rm.clear();

				for(ui l=0;l<dp[j+1].size();l++)
				{
					int r=tc.cmp(dp[j+1][l]);
					if(r==-1)
					{
//						rm.push_back(l);
						dp[j+1][l]=dp[j+1].back();
						l--;
						dp[j+1].pop_back();
					}
					else if(r==1 || r==0) is_need_add=0;
				}
/*
				for(auto it=rm.rbegin();it!=rm.rend();++it)
				{
					dp[j+1].erase(dp[j+1].begin()+*it);
				}
*/
				if(is_need_add) dp[j+1].push_back(tc);
			}
		}
	}

	for(auto tc: dp[k])
	{
		int w;
//		printf("dp %d %d %d\n", tc.c[0], tc.c[1], tc.c[2]);
		w=tc.c[0]/en.c[0];
		for(ui i=1;i<e.size();i++)
		{
			min_u(w, tc.c[i]/en.c[i]);
		}
		min_u(ret, w);
	}

	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;
}