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 main(input) {
  var a = input.split(" ")[0]-0, b = input.split(" ")[1]-0, c = input.split(" ")[2]-0;
  var base = Math.min(a,b);
  for(var i=base;i>=1;i--){
    if(a%i==0 && b%i==0) c--;
    if(c==0) {console.log(i); return}
  }
}

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