p03194 CADDi 2018 for Beginners - Product and GCD
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.

Examples

Input

3 24


Output

2


Input

5 1


Output

1


Input

1 111


Output

111


Input

4 972439611840


Output

206
```python
import math
import collections
# 試し割法

N, P = map(int, input().split())


def trial_division(n):
    # 素因数を格納するリスト
    factor = []
    # 2から√n以下の数字で割っていく
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            factor.append(num)
    # リストが空ならそれは素数
    if not factor:
        return [n]
    else:
        factor.append(n)
        return factor


lst = trial_division(P)
c_lst = collections.Counter(lst)

ans = 1
for k, v in c_lst.items():
    while v >= N:
        ans *= k
        v -= N
print(ans)

```