import sys

sys.setrecursionlimit(10**7)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LI2(): return list(map(int,sys.stdin.readline().rstrip()))
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())
def LS2(): return list(sys.stdin.readline().rstrip())


def prime_factorization(n):  # nの素因数分解
    res = {}
    for i in range(2,int(n**.5)+1):
        if n % i == 0:
            r = 0  # nがiで何回割り切れるか
            while n % i == 0:
                n //= i
                r += 1
            res[i] = r
    if n != 1:
        res[n] = 1
    return res


Q = I()
mod = 10**8+9
for _ in range(Q):
    s,N,K,B = MI()
    X = [s]
    for _ in range(N):
        x = X[-1]
        X.append(1+(x**2+x*12345) % mod)
    factorization = prime_factorization(B)
    prime_factor = list(factorization.keys())
    d = {}
    for p in prime_factor:
        d[p] = []
    for p in prime_factor:
        for i in range(N+1):
            x = X[i]
            r = 0
            while x % p == 0:
                x //= p
                r += 1
            d[p].append((r,i))
    ans = 10**18
    for p in prime_factor:
        A = sorted(d[p])
        Y = [A[i][1] for i in range(N+1)]
        b = 10**18
        for q in prime_factor:
            c = 0
            for j in range(K):
                c += d[q][Y[j]][0]
            b = min(b,c//factorization[q])
        ans = min(ans,b)
    print(ans)