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 Go (1.6) (judge verdict: Accepted)

package main 

import (
  "fmt"
)

func main() {
  var a, b, k int
  fmt.Scan(&a, &b, &k)
  
  var large int

  if a >= b {
    large = a
  } else if a < b{
  	large = b
  }

  ans := 0
  count := 0

  for i := large; i > 0; i-- {
//    fmt.Println("i:",i)
    if a%i == 0 && b%i == 0{
    	ans = i
    	count ++
    }

//    fmt.Println("ans:",ans)
//    fmt.Println("count:",count)
    
    if count == k {
    	break
    }
    
  }
  
  fmt.Println(ans)
}