mod = 10**8+9

def solve():
    seed,n,k,b = map(int,input().split())
    l = []
    p = []
    for i in range(2,b+1):
        if b%i:
            continue
        l.append(i)
        c = 0
        while b%i == 0:
            b //= i
            c += 1
        p.append(c)

    lis = [[] for i in range(len(l))]
    for i in range(n+1):

        now = seed
        for j,m in enumerate(l):
            c = 0
            while now%m == 0:
                now //= m
                c += 1
            lis[j].append(c)
        seed = 1 + (seed*(seed+12345))%mod
    ans = 10**10
    for i,l in enumerate(lis):
        l.sort()
        s = sum(l[:k])
        ans = min(ans,s//p[i])
    return ans


Q = int(input())
for i in range(Q):
    print(solve())