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 <bits/stdc++.h>
#define REP(i, a, n) for (int i = (a); i < (int)(n); ++i)
#define REPC(i, a, n) for (int i = (a); i <= (int)(n); ++i)
#define ALL(t) t.begin(), t.end()
#define RALL(t) t.rbegin(), t.rend()
#define MATINIT(type, row, col, init) \
  vector<vector<type>>(row, vector<type>(col, init));
#define Yes(cond) cout << (cond ? "Yes" : "No") << endl;
#define YES(cond) cout << (cond ? "YES" : "NO") << endl;
using namespace std;
using LL = long long;
using ULL = unsigned long long;
template <class T>
using VEC = std::vector<T>;
template <class T>
using MAT = std::vector<std::vector<T>>;
void DUMP() { cerr << endl; }
template <class Head, class... Tail>
void DUMP(Head &&head, Tail &&... tail) {
  cerr << head << ", ";
  DUMP(std::move(tail)...);
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &vec) {
  os << "{";
  for (auto v : vec) os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, set<T> &s) {
  os << "{";
  for (auto p : s) os << p << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, map<T1, T2> &m) {
  os << "{";
  for (auto p : m) os << p << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> p) {
  os << "[" << p.first << " " << p.second << "]";
  return os;
}
long long gcd(long long a, long long b) { /* the greatest common divisor*/
  while (b != 0) {
    long long r = a % b;
    a = b;
    b = r;
  }
  return a;
}
long long lcm(long long a, long long b) { /*the least common multiple*/
  return (a / gcd(a, b)) * b;
}

int main() {
  int A, B, K;
  cin >> A >> B >> K;
  int g = gcd(A, B);
  int cnt = 0;
  int ans = 0;
  // REP(i, 1, g + 1) {
  //   if (g % i == 0) ++cnt;
  //   if (cnt == K) {
  //     ans = i;
  //     break;
  //   }
  // }
  REP(i, 1, max(A, B) + 1) {
    if (A % i == 0 && B % i == 0) {
      cnt++;
    }
    if (cnt == K) {
      ans = i;
      break;
    }
  }
  cout << ans << endl;
  return 0;
}