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)

'use strict'
// inputに入力データ全体が入る
function Main(input) {
  let inAry = input.split(" ");
  let a = inAry[0];
  let b = inAry[1];
  let k = inAry[2];

  let ayaku = [];
  let byaku = [];
  for(let i = 1; i <= a; i++){
    if(a % i === 0){
      ayaku.push(i);
    }
  }
  for(let i = 1; i <= b; i++){
    if(b % i === 0){
      byaku.push(i);
    }
  }


  let kouyakusu = ayaku.filter((value)=>{
    return byaku.indexOf(value) >= 0;
  })

  kouyakusu = byaku.filter((value)=>{
    return ayaku.indexOf(value) >= 0;
  })

  kouyakusu.sort((a, b) => {
    return a - b;
  });
  console.log(kouyakusu[kouyakusu.length - k]);
}
//*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"));