INF = 2 ** 25
MOD = 100000009
def gen(seed, N):
    x = [0] * (N + 1)
    x[0] = seed
    for n in range(1, N + 1):
        pre = x[n - 1]
        x[n] = 1 + (pre * pre % MOD + pre * 12345) % MOD
    return x
def getFactors(n):
    res = []
    p = 2
    while p * p <= n:
        if n % p == 0:
            e = 0
            while n % p == 0:
                e += 1
                n //= p
            res.append((p, e))
        p += 1
    if n != 1:
        res.append((n, 1))
    return res
def solve(seed, N, K, B):
    x = gen(seed, N)
    factors = getFactors(B)
    res = INF
    for i in range(len(factors)):
        p, e = factors[i]
        y = x[:]
        for j in range(len(y)):
            num = y[j]
            cnt = 0
            while num % p == 0:
                cnt += 1
                num //= p
            y[j] = cnt
        y.sort()
        sum_ = sum(y[:K])
        res = min(res, sum_ // e)
    return res
if __name__ == '__main__':
    Q = int(input())
    for i in range(Q):
        seed, N, K, B = map(int, input().split())
        print(solve(seed, N, K, B))