def solve(s,n,k,b):
    primes = []
    for p in [2,3,5,7,11,13,17,19,23,29,31]:
        if b%p==0: primes.append(p)
    L = len(primes)
    res = [[0]*(n+1) for _ in range(L)]
    ans = 100000000
    for i in range(n+1):
        for j,pj in enumerate(primes):
            ss = s
            c = 0
            while ss%pj==0:
                ss //= pj
                c += 1
            res[j][i] = c
        s = 1+(s*s+s*12345)%100000009
    for j,pj in enumerate(primes):
        bb = b
        c = 0
        while bb%pj==0:
            bb //= pj
            c += 1
        res[j].sort()
        v = sum(res[j][:k])
        ans = min(ans,v//c)
    return ans

Q = int(input())
for _ in range(Q):
    print(solve(*map(int,input().split())))