Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.

To improve his division skills, Oleg came up with $t$ pairs of integers $p_i$ and $q_i$ and for each pair decided to find the greatest integer $x_i$, such that:   $p_i$ is divisible by $x_i$;  $x_i$ is not divisible by $q_i$.  Oleg is really good at division and managed to find all the answers quickly, how about you?


-----Input-----

The first line contains an integer $t$ ($1 \le t \le 50$) — the number of pairs.

Each of the following $t$ lines contains two integers $p_i$ and $q_i$ ($1 \le p_i \le 10^{18}$; $2 \le q_i \le 10^{9}$) — the $i$-th pair of integers.


-----Output-----

Print $t$ integers: the $i$-th integer is the largest $x_i$ such that $p_i$ is divisible by $x_i$, but $x_i$ is not divisible by $q_i$.

One can show that there is always at least one value of $x_i$ satisfying the divisibility conditions for the given constraints.


-----Example-----
Input
3
10 4
12 6
179 822

Output
10
4
179



-----Note-----

For the first pair, where $p_1 = 10$ and $q_1 = 4$, the answer is $x_1 = 10$, since it is the greatest divisor of $10$ and $10$ is not divisible by $4$.

For the second pair, where $p_2 = 12$ and $q_2 = 6$, note that   $12$ is not a valid $x_2$, since $12$ is divisible by $q_2 = 6$;  $6$ is not valid $x_2$ as well: $6$ is also divisible by $q_2 = 6$.  The next available divisor of $p_2 = 12$ is $4$, which is the answer, since $4$ is not divisible by $6$.

Difficulty: competition

Starter code:

Solutions:
mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.readline

    def PrimeDecomposition(N):
        ret = {}
        n = int(N ** 0.5)
        for d in range(2, n + 1):
            while N % d == 0:
                if d not in ret:
                    ret[d] = 1
                else:
                    ret[d] += 1
                N //= d
            if N == 1:
                break
        if N != 1:
            ret[N] = 1
        return ret

    for _ in range(int(input())):
        p, q = list(map(int, input().split()))
        if p % q != 0:
            print(p)
            continue
        prime = PrimeDecomposition(q)
        C = {}
        mi = p
        for pr in prime:
            C = 0
            tmp = p
            while tmp % pr == 0:
                C += 1
                tmp //= pr
            mi = min(mi, pr ** (C - prime[pr] + 1))
        print(p // mi)


def __starting_point():
    main()

__starting_point()

for _ in range(int(input())):
    p, q = list(map(int, input().split()))
    if p % q != 0:
        print(p)
        continue
    pr = {}
    i = 2
    while i*i <= q:
        if q % i == 0:
            x = 0
            while q % i == 0:
                q //= i
                x += 1
            pr[i] = x
        i += 1
    if q != 1:
        pr[q] = 1

    res = 1
    for k in pr:
        v = pr[k]
        pp = p
        x = 0
        while pp % k == 0:
            pp //= k
            x += 1
        res = max(res, p//k**(x-(v-1)))
    print(res)


import sys
input = sys.stdin.readline
for f in range(int(input())):
    p,q=list(map(int,input().split()))
    d=2
    facs=[]
    facsm=[]
    while q>=d*d:
        if q%d==0:
            facs.append(d)
            x=0
            while q%d==0:
                x+=1
                q//=d
            facsm.append(x-1)
        d+=1
    if q>1:
        facs.append(q)
        facsm.append(0)
    mc=p
    pc=p
    for i in range(len(facs)):
        x=0
        while pc%facs[i]==0:
            x+=1
            pc//=facs[i]
        mc=min(mc,facs[i]**(x-min(x,facsm[i])))
    p//=mc
    print(p)


import sys
from sys import stdin

tt = int(stdin.readline())

for loop in range(tt):

    p,q = map(int,stdin.readline().split())

    if p % q != 0:
        print (p)
        continue

    bk = {}
    for i in range(2,10**5):
        if q % i == 0:
            bk[i] = 0
            while q % i == 0:
                bk[i] += 1
                q //= i
        if bk == 1:
            break

    if q != 1:
        bk[q] = 1

    #print (bk)

    ans = float("-inf")
    for i in bk:
        cnt = 0
        tp = p
        while tp % i == 0:
            tp //= i
            cnt += 1
        ans = max(ans , p // (i**(cnt-bk[i]+1)))

    print (ans)