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 (3.8.2) (judge verdict: Wrong Answer)

import numpy as np
from collections import defaultdict
from math import sqrt


def sieve(x):
    primes = []
    is_prime = np.ones(x + 1, bool)
    is_prime[0] = is_prime[1] = False
    for i in range(x + 1):
        if is_prime[i]:
            primes.append(i)
            is_prime[2*i::i] = False

    return primes


def prime_fact(x):
    mx = int(sqrt(x)) + 5
    primes = sieve(mx)
    pf = defaultdict(int)
    for e in primes:
        while x % e == 0:
            x //= e
            pf[e] += 1

    if x != 1:
        pf[x] += 1

    return pf


n, p = map(int, input().split())

pf = prime_fact(p)
ans = 1
for k, v in pf.items():
    if v >= n:
        ans *= k * (v // n)
    else:
        print(1)
        exit()

print(ans)