#!/usr/bin/ python3.8
import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
import numpy as np
MOD = 100000009
Q = int(readline())
SNKB = np.array(read().split(), np.int64)
S = SNKB[::4]
N = SNKB[1::4]
K = SNKB[2::4]
B = SNKB[3::4]

U = 10000
X = np.empty((Q, U + 1), np.uint64)
X[:, 0] = S
for n in range(1, U + 1):
    X[:, n] = (X[:, n - 1] * (X[:, n - 1] + 12345)) % MOD + 1

primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]


def solve(X, N, K, B):
    X = X[:N + 1]

    def solve_p(p):
        nonlocal B
        e = 0
        while B % p == 0:
            B //= p
            e += 1
        A = np.zeros(len(X), np.int32)
        while True:
            q, r = np.divmod(X, p)
            if not np.count_nonzero(r == 0):
                break
            A[r == 0] += 1
            X[r == 0] = q[r == 0]
        A.sort()
        return A[: K].sum() // e
    return min(solve_p(p) for p in primes if B % p == 0)


for x, n, k, b in zip(X, N, K, B):
    print(solve(x, n, k, b))