# 素因数分解
import math

def fac(x):
    L=int(math.sqrt(x))

    FACT=dict()

    for i in range(2,L+2):
        while x%i==0:
            FACT[i]=FACT.get(i,0)+1
            x=x//i

    if x!=1:
        FACT[x]=FACT.get(x,0)+1

    return FACT

def calc(NOW,B):
    A=0
    while NOW%B==0:
        NOW//=B
        A+=1
    return A
    

Q=int(input())
for tests in range(Q):
    seed,N,K,B=map(int,input().split())

    FAC=fac(B)

    NOW=seed
    X=[math.gcd(seed,B)]

    for i in range(N):
        NOW=1+(NOW*NOW+NOW*12345)%100000009
        X.append(math.gcd(NOW,B))

    ANS=1<<60

    for f in FAC:
        X.sort(key=lambda x:calc(x,f))

        AX=0
        NOW=1
        for j in range(K):
            NOW*=X[j]
            while NOW%B==0:
                NOW//=B
                AX+=1
        ANS=min(ANS,AX)
            
    print(ANS)