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 Python (3.4.3) (judge verdict: Runtime Error)

saikyo = [int(i) for i in input().split()] 


number = int(saikyo[1])
bobo = int(saikyo[0])
i = 2
 
answer = ""
 
while number >= i:
    if number % i == 0:
        if answer == "":
            answer = str(i)
        else:
            answer = answer + " " + str(i)
        number /= i
    else:
        i += 1
 
a = [int(i) for i in answer.split()]

import collections

b = collections.Counter(a)
c = len(b)
d = [b.most_common()[i][1] // bobo for i in range(c)]

def remove_specified_values(arr, value):
    while value in arr:
        arr.remove(value)
remove_specified_values(d, 0)

e = len(d)
f = [b.most_common()[i][0] * d[i] for i in range(e)]

import functools
import operator


g = functools.reduce(operator.mul, f)
print(g)