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)

var lines =[];


var readline = require("readline");
var rl = readline.createInterface({
  input:  process.stdin,
  output: process.stdout
});

rl.on('line',function(x){
  lines.push(x);
});

rl.on('close',function(){

  var tmp = lines[0].split(" ");
  
  var a = Number(tmp[0]);
  var b = Number(tmp[1]);
  var k = Number(tmp[2]);
  var counter = 0;


    for(var i=100;i>=1;i--){
        if(a%i === 0 && b%i === 0){counter++;}
        if(counter === k){console.log(i); break;}
    }

});