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").map(Number);
  input.shift();
  var n = arrsum(input);
  if(n==input.length){
  n = 1;
  }
  if(arrsum2(input)%2==1) n=1;
  
  if(n%2==1){
  console.log("first");
  }else{
  console.log("second");
  }
}Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());
function arrsum(arr){
    var sum = 0;
    for (var i=0,len=arr.length; i<len; ++i) {
        sum += arr[i];
    };
    return sum;
}
function arrsum2(arr){
    var sum = 0;
    for (var i=0,len=arr.length; i<len; ++i) {
        if(arr[i]!=1)sum += arr[i];
    };
    return sum;
}