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>
using namespace std;
#define ll long long
inline ll read() {
    ll x=0,f=1; char ch=getchar();
    for(;ch<'0'||ch>'9';ch=getchar())
        if(ch=='-')f=-f;
    for(;ch>='0'&&ch<='9';ch=getchar())
        x=x*10+ch-'0';
    return x*f;
}
inline void chkmin( int &a,int b ) { if(a>b) a=b; }
inline void chkmax( int &a,int b ) { if(a<b) a=b; }
#define _ read()
inline int gcd( int a,int b ) { return b==0?a:gcd(b,a%b); } 
int main() {
	int a=_,b=_,c=_;
	for( int i=1;i<=min(a,b);i++ ) {
		if(max(a,b)%i==0) c--;
		if(!c) return cout<<i<<"\n",0;
	}
}