from math import sqrt
from collections import defaultdict
def PrimeFactorization1(N):
    ret = defaultdict(int)
    for i in range(2,int(sqrt(N))+1):
        while N % i == 0:
            ret[i] += 1
            N //= i
    if N > 1:
        ret[N] += 1
    return ret

def PrimeFactorization2(N, L):
    ret = defaultdict(int)
    for p in L:
        while N % p == 0:
            ret[p] += 1
            N //= p
    return ret

mod = 10**8+9
Q = int(input())
for _ in range(Q):
    seed,N,K,B = map(int,input().split())
    X = [seed]
    for i in range(N):
        X.append(((X[i] * X[i]) + (X[i] * 12345)) % mod + 1)
    BP = PrimeFactorization1(B)
    L = list(BP.keys())
    XP = []
    for i in range(N+1):
        XP.append(PrimeFactorization2(X[i], L))
    ans = 1<<64
    for p in L:
        P = []
        for i in range(N+1):
            P.append(XP[i][p])
        P.sort()
        cnt = 0
        for i in range(K):
            cnt += P[i]
        ans = min(ans, cnt // BP[p])
    print(ans)