import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;

/**
 * yukicoder no.28
 * @author scache
 *
 */
public class Main {
	private final long MOD = 100000009;

	public static void main(String[] args) {
		Main p = new Main();
	}

	public Main() {
		Scanner sc = new Scanner(System.in);
		int q = sc.nextInt();
		for(int i=0;i<q;i++)
			System.out.println( solve(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt()) );
	}
	
	public int solve(int seed, int n, int k, int b) {
		long[] x = new long[n+1];
		x[0] = seed;
		for(int i=1;i<x.length;i++)
			x[i] = 1 + (x[i-1]*(x[i-1]+12345)) % MOD;
		
		int res = Integer.MAX_VALUE;
		ArrayList<Factor> factors = getFactorList(b);
//		for(int i=0;i<factors.size();i++)
//			System.out.println(factors.get(i).prime +" " + factors.get(i).num);
		
		for(int i=0;i<factors.size();i++){
			int[] counts = new int[n+1];
			for(int j=0;j<x.length;j++){
				int c = 0;
				int p = factors.get(i).prime;
				
				while(x[j]%p == 0){
					x[j] /= p;
					c++;
				}
				counts[j] = c;
			}
			
			Arrays.sort(counts);
			int sum = 0;
			for(int j=0;j<k;j++)
				sum += counts[j];
			
			res = Math.min(res, sum/factors.get(i).num);
		}
		
		return res;
		
	}
	
	private ArrayList<Factor> getFactorList(int b){
		ArrayList<Factor> l = new ArrayList<Factor>();
		
		for(int i=2;i*i<=b;i++){
			int num = 0;
			while(b%i==0){
				b/=i;
				num++;
			}
			
			if(num>0)
				l.add(new Factor(i, num));
		}
		
		if(b!=1)
			l.add(new Factor(b, 1));
		
		return l;
	}
	
	public class Factor {
		int prime;
		int num;
		
		public Factor(int prime, int num) {
			this.prime = prime;
			this.num = num;
		}
	}

}