import sys

read=sys.stdin.buffer.read
readline=sys.stdin.buffer.readline

fac=[0,1]
for b in range(2, 37):
    p=2
    ps=[]
    bb=b
    while p*p<=bb:
        if bb%p==0:
            cnt=0
            while bb%p==0:
                bb//=p
                cnt+=1
            ps.append([p,cnt])
        p+=1
    if bb!=1: ps.append([bb,1])
    fac.append(ps)

MOD=10**8+9 
for _ in range(int(readline())):
    seed,N,K,B=map(int,readline().split())
    X=[seed]
    now=seed
    for i in range(1,N+1): 
        now=1+(now*(now+12345))%MOD
        X.append(now)
    ans=MOD
    for p, cntb in fac[B]:
        arr=[]
        for xi in X:
            c=0
            while xi%p==0:
                xi//=p
                c+=1
            arr.append(c)
        arr.sort()
        ans=min(ans,sum(arr[:K])//cntb)
    print(ans)