fact = [0,1]
for b in range(2, 37):
    ps = []
    for p in range(2, 32):
        cnt = 0
        while b % p == 0:
            cnt += 1
            b //= p
        if cnt:
            ps.append((p, cnt))
    fact.append(ps)

for _ in range(int(input())):
    seed, n, k, b = map(int, input().split())
    x = [seed]
    now = seed
    for i in range(n):
        now = 1 + (now * (now + 12345)) % 100000009
        x.append(now)
    ans = 10 ** 9
    for p, cntb in fact[b]:
        cntx = []
        for xi in x:
            cnt = 0
            while xi % p == 0:
                cnt += 1
                xi //= p
            cntx.append(cnt)
        cntx.sort()
        ans = min(ans, sum(cntx[:k]) // cntb)
    print(ans)