using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Diagnostics;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using Enu = System.Linq.Enumerable;

class Program
{
    static readonly int Mod = (int)1e8 + 9;

    void Solve()
    {
        int Q = reader.Int();
        for (int qi = 0; qi < Q; qi++)
        {
            int seed = reader.Int(), N = reader.Int(), K = reader.Int(), B = reader.Int();
            int ans = MinZeros(seed, N, K, B);
            Console.WriteLine(ans);
        }
    }

    private int MinZeros(int seed, int N, int K, int B)
    {
        long[] A = new long[N + 1];
        A[0] = seed;
        for (int i = 1; i <= N; i++)
            A[i] = 1 + (A[i - 1] * A[i - 1] + A[i - 1] * 12345) % Mod;

        var factors = Factorization(B);
        int min = int.MaxValue;
        foreach (int p in factors.Keys)
        {
            int[] count = new int[N + 1];
            for (int i = 0; i <= N; i++)
                for (int t = (int)A[i]; t % p == 0; t /= p)
                    count[i]++;
            Array.Sort(count);
            int d = 0;
            for (int i = 0; i < K; i++)
                d += count[i];
            d /= factors[p];
            min = Math.Min(min, d);
        }
        return min;
    }

    static Dictionary<int, int> Factorization(int n)
    {
        var dic = new Dictionary<int, int>();
        for (int i = 2; i * i <= n; i++)
        {
            while (n % i == 0)
            {
                n /= i;
                if (!dic.ContainsKey(i)) dic[i] = 1;
                else dic[i]++;
            }
        }
        if (n > 1) dic[n] = 1;
        return dic;
    }


    Reader reader = new Reader(Console.In);
    static void Main() { new Program().Solve(); }
}

class Reader
{
    private readonly TextReader reader;
    private readonly char[] separator = { ' ' };
    private readonly StringSplitOptions removeOp = StringSplitOptions.RemoveEmptyEntries;
    private string[] A = new string[0];
    private int i;

    public Reader(TextReader r) { reader = r; }
    public bool HasNext() { return Enqueue(); }
    public string String() { return Dequeue(); }
    public int Int() { return int.Parse(Dequeue()); }
    public long Long() { return long.Parse(Dequeue()); }
    public double Double() { return double.Parse(Dequeue()); }
    public int[] IntLine() { var s = Line(); return s == "" ? new int[0] : Array.ConvertAll(Split(s), int.Parse); }
    public int[] IntArray(int N) { return Enu.Range(0, N).Select(i => Int()).ToArray(); }
    public int[][] IntGrid(int H) { return Enu.Range(0, H).Select(i => IntLine()).ToArray(); }
    public string[] StringArray(int N) { return Enu.Range(0, N).Select(i => Line()).ToArray(); }
    public string Line() { return reader.ReadLine().Trim(); }
    private string[] Split(string s) { return s.Split(separator, removeOp); }
    private bool Enqueue()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return Enqueue();
        A = Split(line);
        i = 0;
        return true;
    }
    private string Dequeue() { Enqueue(); return A[i++]; }
}