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: Wrong Answer)

N,P = map(int,input().split(' '))
#N=3
#P=24


def primes(n):
	f = [True]*n
	f[0] = False
	f[1] = False
	m = int(n**0.5+1)
	for i in range(2,m):
		if f[i]:
			for j in range(i*i,n, i):
				f[j] = False
	return f



if N == 1:
	print(P)
	exit()

sP=int(P**0.5)+1
f = primes(sP)
prime = [x for x in range(1,sP) if f[x]]

ans = 1
for p in prime:
	if P % (p**N) == 0:
		ans*=p
print(ans)