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.
from sys import stdin
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
 
class FastIO(IOBase):
    newlines = 0
 
    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None
 
    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()
 
    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()
 
    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)
 
 
class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")
 
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
def inp():
    return int(input())
def arrinp():
    return list(map(int,input().split()))
######################
#start code from here#
######################
import math
from math import ceil, gcd
def main():
    for _ in range(inp()):
        p,q = arrinp()
        if(q>p):
            print(p)
            continue
        if(p%q != 0):
            print(p)
            continue
        if(p==q):
            i = 2
            while(p%i!=0):
                i += 1
            print(p//i)
            continue
        #p>q and p is multiple of q
        factors = primeFactors(q)
        ans = 1
        for fc in factors:
            c= p//fc
            while(c%fc==0):
                c = c//fc
            c = c*(fc**(factors[fc]-1))
            ans = max(ans, c)
        print(ans)

def primeFactors(n): 
    primes = dict()
    while n % 2 == 0: 
        primes[2] = primes.get(2,0)+1
        n = n // 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            primes[i] = primes.get(i,0)+1
            n = n // i 
    if n > 2: 
        primes[n] = primes.get(n,0)+1
    return primes
if __name__ == '__main__':
    main()
"""
2
873935277189052612 530795521
559754147245184151 431517529
"""
'''answers
37932865019708
26946235365387
'''

"""
2
873935277189052612 530795521
559754147245184151 431517529
{2: 2, 1787: 1, 23039: 2, 230339: 1} for p not q
{23039: 2}
23039 530795521 2
1646463172
{3: 1, 13: 1, 23: 1, 61: 1, 151: 1, 157: 1, 20773: 2} for p not q
{20773: 2}
20773 431517529 2
1297175919
"""