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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input) {
  input = input.split("\n");
  var N = parseInt(input[0].split(" ")[0]);
  var P = parseInt(input[0].split(" ")[1]);
  A = new Array();
  P2=Math.ceil(P/2);
  var j=-1;
  var k=0;
  for(i=2;i<P2;i){
    if(P%i==0){
      if(k==0){
        j++;
      }
      k++;
      A[j]=[i,k];
      P=P/i;
    }else{
      i++;
      k=0;
    }
    if(P==1){
      break;
    }
  }
  var ans=1;
  for(i=0;i<A.length;i++){
    ans*=Math.max(Math.floor(A[i][1]/N)*A[i][0],1);
  }

  console.log('%s', ans);
}
  
// "実行する"ボタンを押した時に実行される関数 (デバッグ用)
function debug(){
  var input = document.getElementById("input").value;
  Main(input);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));