import sys

sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
# inf = 18446744073709551615
inf = 4294967295
# md = 10**9+7
# md = 998244353
md = 10**8+9

def prime_factorization(a):
    pp, ee = [], []
    if a & 1 == 0:
        pp += [2]
        ee += [0]
        while a & 1 == 0:
            a >>= 1
            ee[-1] += 1
    p = 3
    while p**2 <= a:
        if a%p == 0:
            pp += [p]
            ee += [0]
            while a%p == 0:
                a //= p
                ee[-1] += 1
        p += 2
    if a > 1:
        pp += [a]
        ee += [1]
    return pp, ee

from collections import defaultdict

def solve():
    x, n, k, b = LI()
    pp, ee = prime_factorization(b)
    ptoe = defaultdict(list)
    for _ in range(n+1):
        y = x
        for p in pp:
            s = 0
            while y%p == 0:
                y //= p
                s += 1
            ptoe[p].append(s)
        x = 1+(x**2%md+x*12345%md)%md

    ans = inf
    for p, e in zip(pp, ee):
        ptoe[p].sort()
        ans = min(ans, sum(ptoe[p][:k])//e)

    print(ans)

for case in range(II()):
    solve()