Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def sol(x):
  num = P
  cnt = 0
  while cnt<N:
    if cnt<=N-2:
      if num%(x**3)!=0:return False
      else:num/=x**3
      cnt+=3
    else:
      if num%x!=0:return False
      else:num/=x
      cnt += 1
  return True
  

N,P=map(int,input().split())
for x in range(int(P**(1/N))+1,0,-1):
  if sol(x):
    print(x)
    exit()