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.
def sieve(n):
	prime = [-1]*(n+1)
	for i in range(2,n+1):
		if prime[i]==-1:
			for j in range(i,n+1,i):
				prime[j] = i
	return prime

prime = sieve(100010)
for nt in range(int(input())):
	p,q = map(int,input().split())
	if p>q:
		if p%q!=0:
			print (p)
		else:
			primes = []
			for i in range(2,int(q**0.5)+2):
				if q%i==0:
					primes.append(i)
					if q//i!=1:
						primes.append(q//i)
			ans = 1
			if not primes:
				primes.append(q)
			# print (primes)
			for i in primes:
				k = 1
				while p%(i**k)==0:
					# print (p//(i**k))
					if (p//(i**k))%q!=0:
						ans = max(ans, p//(i**k))
						break
					k += 1
			print (ans)

	elif p==q:
		num = -1
		for i in range(2,int(p**0.5)+1):
			if p%i==0:
				num = i
				break
		if num==-1:
			print (1)
		else:
			print (p//num)
	else:
		print (p)