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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
#define MOD 1000000007
#define MAX(a,b) (a>b?a:b)
#define MAX3(a,b,c) MAX(a,MAX(b,c))
#define MIN(a,b) (a<b?a:b)
#define MIN3(a,b,c) MIN(a, MIN(b,c))
typedef long long lli;
int cmp(const void *a, const void *b) {
    return *(int*)a - *(int*)b;
}


int main()
{
    int a, b, k, i, cnt=0;
    scanf("%d%d%d",&a,&b,&k);
    for(i=MIN(a,b); cnt<k; i--) {
        if(a%i==0 && b%i==0) {
            cnt++;
        }
    }
    printf("%d",i+1);
    return 0;
}