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 ≤ t ≤ 50) — the number of pairs.

Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 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.
import sys
import  random

input = sys.stdin.readline


def gcd(a, b):
    if a == 0:
        return b
    return gcd(b % a, a)


def lcm(a, b):
    return (a * b) / gcd(a, b)

def main():
    for _ in range(int(input())):
        # n=int(input())
        # a=list(map(int, input().split()))
        p,q=map(int, input().split())
        # p=random.randint(2,1000)
        # q=random.randint(3,10)
        orp = p
        orq = q
        # print(p,q)
        if p%q!=0:
            print(p)
        else:
            a=[]
            for i in range(2,int(q**0.5)+1):
                if q%i==0:
                    a.append(i)
                    a.append(q//i)
            #a.sort()
            a.append(q)
            b=[]
            for i in a:
                k=p
                while(k%q==0):
                    k//=i

                b.append(k)
            print(max(b))

            # c=0
            # while(p%q==0):
            #     c+=1
            #     p//=q
            # a=[]
            # i=2
            # i=2
            # while(i*i<=q):
            #     while(q%i==0):
            #         q//=i
            #         a.append(i)
            #     i+=1
            # a.sort()
            # if q>2:
            #     a.append(q)
            # print(p,c,a)
            # #p=orp
            # q=orq
            # for i in range(len(a)-1,-1,-1):
            #     print(a[i])
            #     for j in range(c):
            #         if ((p*a[i])%q!=0):
            #             #print(i, j)
            #             p*=a[i]
            #         else:
            #             z=(p*a[i])//q
            #             p*=a[i]
            #             p//=min(z,a[i])
            # ans1=p
            # #print(ans1)
            # p=orp
            # q=orq
            # f=0
            # for i in range(p,0,-1):
            #     if p%i==0 and i%q!=0:
            #         if ans1==i:
            #             f=1
            #             print('ok')
            #         else:
            #             print('no',ans1,i)
            #         break
            # # if f==0:
            # #     print('N0')
            # #     print(orp,orq,ans1)
            # #     break



    return

if __name__=="__main__":
    main()

