Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

function search_nums(left, right){// left < right
  nums = [];
  for( var i=0 ; i<left ; i++ ){
    num = left-i;
    if((left%num==0) && (right%num==0)){
      nums.push(num);
    }
  }
  return nums;
}

function main(input) {
  const formatted_input = input.split(' ').map( x => parseInt(x, 10) );
  const A = formatted_input[0];
  const B = formatted_input[1];
  const K = formatted_input[2];



  if(A <= B){
    console.log(search_nums(A, B)[K-1]);
  }else{
    console.log(search_nums(B, A)[K-1]);
  }
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));