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: Time Limit Exceeded)

n,p = (int(i) for i in input().split())
prime=[]
def prime_judge(p):
    isPrime=True
    for i in range(1,p):
        if p%i==0 and i!=1:
            isPrime = False
    return isPrime

if p>1:
    for i in range(2,p):
        if prime_judge(i):
            prime.append(i)

    i=0
    factor={}
    while(i<len(prime) and p>1):
        divided = False
        if p%prime[i]==0:
            p/=prime[i]
            divided = True
            if(prime[i] in factor.keys()):
                factor[prime[i]] += 1
            else:
                factor[prime[i]] = 1
        if not divided:
            i += 1

    sum = 1
    for i,x in factor.items():
        if x>=n:
            sum *= i**(int(x/n))
    print(int(sum))
else:
    print(1)