import math

def isprime(a):
    b = int(math.sqrt(a))
    for i in range(2, b):
        if a % i == 0:
            return False
    return True

Q = int(input())

for i in range(Q):
    seed, N, K, B = map(int, input().split())
    N += 1
    X = []
    X.append(seed)
    for j in range(N):
        X.append(1 + (X[j] * X[j] + X[j] * 12345) % 100000009)

    ans = 99999999
    for j in range(2, B + 1):
        if not isprime(j):
            continue
        if B % j != 0:
            continue
        div = 0
        tmpB = B
        while(B % j == 0):
            B = B // j
            div += 1
        ar = [0] * N
        for k in range(N):
            tmp = X[k]
            while tmp % j == 0:
                ar[k] += 1
                tmp = tmp // j

        ar.sort()

        mul = 0
        for k in range(K):
            mul += ar[k]

        ans = min(ans, mul // div)

    print(ans)