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)


import collections

# def get_lim(n):
#     # for i in range(n):
#     #     if i * i > n:
#     #         return i + 1
#     return pow(10, int((len(str(n)) / 2)))

def prime_factor(n, length):
    ass = collections.defaultdict(int)
    # break_num = pow()
    # for i in range(2,int(n**0.5)+1):
    # lim = get_lim(n)
    for i in range(2, n):
        # print(pow(i, length),  n)
        # if pow(i, length) > n:
        #     break
        if i > n or n == 1:
            break
        # print(n, i)
        # i = pow(i, num)
        while n % i==0:
            ass[i] += 1
            n = n//i

    if n != 1:
        ass[n] += 1
    return ass

if __name__ == '__main__':
    length, num = list(map(int, input().split()))

    if length == 1:
        print(num)
    else:

        soinnsuu = prime_factor(num, length)
        ans = 1
        # print(soinnsuu)
        for data in soinnsuu.keys():
            if soinnsuu[data] >= length:
               ans *= data
        print(ans)