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
    tmp int
  )
  fmt.Scan(&a)
  fmt.Scan(&b)
  fmt.Scan(&k)

  tmp = a
  if a > b {
    tmp = b;
  }

  count:=0
  for i:=tmp;i>0;i-- {
    if a % i == 0 && b % i == 0 {
      count++
    }
    if count == k {
      fmt.Println(i)
      break
    }
  }
}