from collections import *
from itertools import *
from functools import *
from heapq import *
import sys,math
input = sys.stdin.readline
mod = 10**8 + 9
P = [2,3,5,7,11,13,17,19,23,29,31]
def answer():
    seed,N,K,B = map(int,input().split())
    X = [seed]
    for _ in range(N):
        seed = 1 + (seed**2 + seed*12345)%mod
        X.append(seed)
    
    Z = []
    for p in P:
        while B%p==0:
            B //= p
            Z.append(p)
    C = Counter(Z)
    ans = 1<<60
    for k,v in C.items():
        Y = []
        for x in X:
            y = x
            tmp = 0
            while y%k==0:
                tmp += 1
                y //= k
            Y.append(tmp)
        Y.sort()
        ans = min(ans,sum(Y[:K])//v)

    print(ans)
    
for _ in range(int(input())):
    answer()