# 素因数分解
import math
from operator import itemgetter
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

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

FAC=[dict() for i in range(40)]

for x in range(2,40):
    FAC[x]=fac(x)

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

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

    LIST=list(FAC[B])
    LEN=len(LIST)

    NOW=seed
    X=[[0]*LEN for i in range(N+1)]

    for i in range(LEN):
        X[0][i]=calc(NOW,LIST[i])

    for i in range(N):
        NOW=1+(NOW*NOW+NOW*12345)%100000009

        for j in range(LEN):
            X[i+1][j]=calc(NOW,LIST[j])

    ANS=1<<30

    for i in range(LEN):
        X.sort(key=itemgetter(i))

        Y=0
        for j in range(K):
            Y+=X[j][i]

        ANS=min(ANS,Y//FAC[B][LIST[i]])
        
    print(ANS)