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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from collections import defaultdict
from math import sqrt
N,P = map(int, input().split())
is_prime = [True]*(10**6+1)
is_prime[0] = is_prime[1] = False
def sieve(n:int):
    """Sieve of Eratoshenes
    return the number of prime number (0, n]"""
    global is_prime
    for i in range(2, n+1):
        if is_prime[i]:
            # 素数の倍数は合成数
            for j in range(i*2, n+1, i):
                is_prime[j] = False

sieve(10**6)
facts = defaultdict(lambda:0)
p = P
for i in range(int(sqrt(P))):
    if not is_prime[i]:
        continue
    if p == 1:
        break
    while p % i == 0:
        p //= i
        facts[i] += 1
ans = 1
for k,v in facts.items():
    ans *= pow(k, v//N)
print(ans)