def is_prime(a):
    i = 2
    while i * i <= a:
        if a % i == 0:
            return False
        i += 1

    return True

def main():
    Q = int(input())
    for _ in range(Q):
        seed, N, K, B = map(int, input().split())
        N += 1
        X = [0] * N
        X[0] = seed
        for i in range(1, N):
            X[i] = 1 + (X[i - 1] * X[i - 1] + X[i - 1] * 12345) % 100000009

        ans = float('inf')
        for p in range(2, B + 1):
            if not is_prime(p):
                continue
            if B % p != 0:
                continue
            div = 0
            while B % p == 0:
                B = B // p
                div += 1

            ar = [0] * N
            for i in range(N):
                temp = X[i]
                while temp % p == 0:
                    ar[i] += 1
                    temp = temp // p

            ar.sort()

            mul = 0
            for i in range(K):
                mul += ar[i]
            ans = min(ans, mul // div)
        print(ans)

if __name__ == '__main__':
    main()