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)

// inputに入力データ全体が入る
function Main(input) {
    input = input.split("\n");
    tmp = input[0].split(" ");
    const a = parseInt(tmp[0], 10);
    const b = parseInt(tmp[1], 10);
    const c = parseInt(tmp[2], 10);
    
    //console.log(a,b,c);
    function divisor(num){
    var results = [];
   for(var i=1; i<=num; i++) {
        if( (num%i == 0) ) {
            results.push(i);
        }
    }
    return results;

    }
// テスト
p = divisor(a);
//console.log(p);
  q = divisor(b);
//console.log(q);
p1=p.length;q1=q.length;
//console.log(p1,q1);
var cnt =0;

ppp = [];qqq=[];
  if (p1 >= q1){
     for(i = 0;i<q1;i++){
      for (l=i;l<p1;l++){ if(q[i]==p[l]){ppp[cnt] = p[l];
                                     cnt =cnt +1;
                                   //  console.log(ppp);
                                     break; }
                                       
                        }
                       }
                   }
  else   
    { for(i = 0;i<p1;i++){
      for (l=i;l<q1;l++){ if(p[i]==q[l]){ppp[cnt] = q[l];
                                     cnt =cnt +1;
                                  //   console.log(ppp);
                                     break; }
                         }
                         } 
                        }
                
    t =ppp.length; 
//  console.log(t-c);
    var t=t-c;
    console.log(ppp[t]);     
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));