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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <iostream>
#include <queue>
#include <unordered_map>
#include <cmath>
#include <queue>
#include <string>
#include <random>
using namespace std;
typedef long long ll;
const int maxn = 100005;

int main() {
#ifdef suiyuan2009
  freopen("/Users/suiyuan2009/CLionProjects/icpc/input.txt", "r", stdin);
  //freopen("/Users/suiyuan2009/CLionProjects/icpc/output.txt", "w", stdout);
#endif
  int a,b,c;
  cin>>a>>b>>c;
  int cnt=0;
  for(int i=1;i<=a&&i<=b;i++){
    if(a%i==0&&b%i==0)cnt++;
    if(cnt==c){
      cout<<i<<endl;
      break;
    }
  }
  return 0;
}