import sys
import math
import bisect
from heapq import heapify, heappop, heappush
from collections import deque, defaultdict, Counter
from functools import lru_cache
from itertools import accumulate, combinations, permutations, product

sys.setrecursionlimit(1000000)
MOD = 10 ** 9 + 7
MOD99 = 998244353

input = lambda: sys.stdin.readline().strip()
NI = lambda: int(input())
NMI = lambda: map(int, input().split())
NLI = lambda: list(NMI())
SI = lambda: input()
SMI = lambda: input().split()
SLI = lambda: list(SMI())
EI = lambda m: [NLI() for _ in range(m)]


# 高速エラストテネス　sieve[n]はnの最小の素因数
def make_prime_table(n):
    sieve = list(range(n + 1))
    sieve[0] = -1
    sieve[1] = -1
    for i in range(4, n + 1, 2):
        sieve[i] = 2
    for i in range(3, int(n ** 0.5) + 1, 2):
        if sieve[i] != i:
            continue
        for j in range(i * i, n + 1, i * 2):
            if sieve[j] == j:
                sieve[j] = i
    return sieve

prime_table = make_prime_table(100000)
# 素数列挙
primes = [p for i, p in enumerate(prime_table) if i == p]

# 素因数分解　上のprime_tableと組み合わせて使う
def prime_factorize(n):
    result = []
    while n != 1:
        p = prime_table[n]
        e = 0
        while n % p == 0:
            n //= p
            e += 1
        result.append((p, e))
    return result


# Nの素因数分解を辞書で返す(単体)
def prime_fact(n):
    root = int(n**0.5) + 1
    prime_dict = {}
    for i in range(2, root):
        cnt = 0
        while n % i == 0:
            cnt += 1
            n = n // i
        if cnt:
            prime_dict[i] = cnt
    if n != 1:
        prime_dict[n] = 1
    return prime_dict

# 約数列挙（単体）
def divisors(x):
    res = set()
    for i in range(1, int(x**0.5) + 2):
        if x % i == 0:
            res.add(i)
            res.add(x//i)
    return res


def main():
    Q = NI()
    INF = 100000000
    for _ in range(Q):
        s, N, K, B = NMI()
        X = [s]
        for i in range(N):
            x = X[-1]
            nx = 1 + (x**2 + x * 12345) % (10**8+9)
            X.append(nx)
        P = prime_fact(B)
        ans = INF
        for p, k in P.items():
            Xp = []
            for i, x in enumerate(X):
                r = 0
                nx = x
                while nx % p == 0:
                    nx //= p
                    r += 1
                Xp.append(r)
            Xp.sort()
            ans = min(ans, sum(Xp[:K]) // k)
        
        print(ans)



if __name__ == "__main__":
    main()