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: Accepted)

#include<bits/stdc++.h>
using namespace std;


/// File input & output /////
#define fRead(x)        freopen("x.txt","r",stdin)
#define fWrite(x)       freopen ("x.txt","w",stdout)


#define ld              long double
#define ll              long long
#define ull             unsigned long long
#define ff              first
#define ss              second
#define pb              push_back
#define INF             2e16
#define PI              acos(-1.0)
#define mp              make_pair
#define pii             pair<int,int>
#define pll             pair<LL,LL>


#define min3(a,b,c)     min(a,min(b,c))
#define max3(a,b,c)     max(a,max(b,c))
#define min4(a,b,c,d)   min(a,min(b,min(c,d)))
#define max4(a,b,c,d)   max(a,max(b,max(c,d)))
#define SQR(a)          ((a)*(a))
#define FOR(i,a,b)      for(int i=a;i<=b;i++)
#define ROF(i,a,b)      for(int i=a;i>=b;i--)
#define REP(i,b)        for(int i=0;i<b;i++)
#define MEM(a,x)        memset(a,x,sizeof(a))
#define ABS(x)          ((x)<0?-(x):(x))

#define SORT(v)         sort(v.begin(),v.end())
#define REV(v)          reverse(v.begin(),v.end())


#define FASTIO        ios_base::sync_with_stdio(0);cin.tie(nullptr);




///..................Sort by second element in a pair in decending order............. ///
bool SortbySecDesc(const pair<long long,long long > &a, const pair<long long,long long > &b)
{
    return a.second>b.second;
}

///.........................first element of pair in descending order..........................//////
bool sortinrev(const pair<int,int> &a,
               const pair<int,int> &b)
{
       return (a.first > b.first);
}



///.............................................................TEMPLATE................................................./////

int main()
{
    FASTIO;

    int a , b , k;

    cin >> a >> b >> k;


    ll ans = max(a,b);

    vector<int>v;


    for(int i=1; i<=ans; i++)
    {
        if((a%i==0 && b%i==0))
        {
            v.pb(i);
        }
    }

    cout << v[v.size()-k] << endl;





    return 0;
}