import sys
input = sys.stdin.readline
from operator import itemgetter

FAC=[{}, {}, {2: 1}, {3: 1}, {2: 2}, {5: 1}, {2: 1, 3: 1}, {7: 1}, {2: 3}, {3: 2}, {2: 1, 5: 1}, {11: 1}, {2: 2, 3: 1}, {13: 1}, {2: 1, 7: 1}, {3: 1, 5: 1}, {2: 4}, {17: 1}, {2: 1, 3: 2}, {19: 1}, {2: 2, 5: 1}, {3: 1, 7: 1}, {2: 1, 11: 1}, {23: 1}, {2: 3, 3: 1}, {5: 2}, {2: 1, 13: 1}, {3: 3}, {2: 2, 7: 1}, {29: 1}, {2: 1, 3: 1, 5: 1}, {31: 1}, {2: 5}, {3: 1, 11: 1}, {2: 1, 17: 1}, {5: 1, 7: 1}, {2: 2, 3: 2}, {37: 1}, {2: 1, 19: 1}, {3: 1, 13: 1}]

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)