def solve(s,n,k,b):
    res = [0]*(n+1)
    for i in range(n+1):
        res[i] = s
        s = 1+(s*s+s*12345)%100000009
    ans = 100000000
    for p,t in fac[b]:
        val = [0]*(n+1)
        for i,si in enumerate(res):
            c = 0
            while si%p==0:
                si //= p
                c += 1
            val[i] = c
        val.sort()
        ans = min(ans,sum(val[:k])//t)
    return ans

fac = [[] for _ in range(37)]
for b in range(2,37):
    for p in [2,3,5,7,11,13,17,19,23,29,31]:
        c = 0
        bb = b
        while bb%p==0:
            c += 1
            bb //= p
        if c: fac[b].append((p,c))

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