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 factors(x):
	d = {}
	temp = 0
	while(x%2 == 0):
		temp += 1
		x = x//2
	if(temp):
		d[2] = temp
	
	for i in range(3, int(x**0.5)+1):
		temp = 0
		while(x%i == 0):
			temp += 1
			x = x//i
			
		if(temp):
			d[i] = d.get(i, 0) + temp
			
	if(x > 1):
		d[x] = d.get(x, 0) + 1
		
	return d

for u in range(int(input())):
	p, q = map(int, input().split())
	if(p%q):
		print(p)
	else:
		x = factors(q)
		#print(x)
		ans = 10**19
		for i in x:
			temp = 0
			k = p
			while(k%i == 0):
				temp += 1
				k = k//i
			#print(i, i**(temp - x[i] + 1))
			ans = min(ans, i**(temp - x[i] + 1))
			
		print(p//ans)