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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <map>

int main()
{
  long long n, p;
  std::cin >> n >> p;
  std::map<long long, int> cnt;
  long long rest = p;
  for (long long i = 2; i * i <= p; i++) {
    while (rest % i == 0) {
      rest = rest / i;
      cnt[i]++;
    }
  }
  cnt[rest]++;
  long long result = 1;
  for (const auto& x : cnt) {
    if (n <= x.second) {
      result = result * x.first * (x.second / n);
    }
  }
  std::cout << result << std::endl;
  return 0;
}