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) {
    input = input.split(" ").map(Number);
    var sum = 0;
    for(var i=Math.min(input[0],input[1]);true;i--){
        if(input[0]%i==0&&input[1]%i==0) sum++;
        if(sum == input[2]){
            console.log(i);
            break;
        }
    }
}Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());