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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using static System.Console;
using static System.Math;
 
public class Hello{
    static public int mod = 1000000007;
    public static void Main(){
        // 方針
        // 
        int[] n = inta();
        int count = 0;
        for(int i=Max(n[0],n[1]);i>=0;i--){
            if(n[0] %i == 0&& n[1]%i == 0){
                count++;
            }
            if(count == n[2]){
                WriteLine(i);
                break;
            }
        }
        


        
        
        
    }
    static void unionfind(ref int[] uni,int a,int b){
        var memo = new List<int>();
        memo.Add(a);
        memo.Add(b);
        int min = Min(a,b);
        while(uni[a] != a){
            a = uni[a];
            memo.Add(a);
        }
        while(uni[b] != b){
            b = uni[b];
            memo.Add(b);
        }
        min = Min(min,a);
        min = Min(min,b);
        foreach(var k in memo){
            uni[k] = min;
        }
    }
    static int unionfind2(ref int[] uni,int a){
        var memo = new List<int>();
        memo.Add(a);
        while(uni[a] != a){
            a = uni[a];
            memo.Add(a);
        }
        foreach(var k in memo){
            uni[k] = a;
        }
        return a;
    }
    static int binarysearchd(int[] a,int b){
        int leng = a.Length;
        int min = 0;
        int max = leng-1;
        while(max - min > 1){
            int mid = (min+max)/2;
            if(a[mid] < b){
                min = mid;
            }else{
                max = mid;
            }
        }
        if(a[0] >= b){
            return 0;
        }else if(a[leng-1] < b){
            return leng;
        }else{
            if(a[max] < b){
                return max+1;
            }
            return min+1;
        }
    }
    static int binarysearchu(int[] a,int b){
        int leng = a.Length;
        int min = 0;
        int max = leng-1;
        while(max - min > 1){
            int mid = (min+max)/2;
            if(a[mid] < b){
                min = mid;
            }else{
                max = mid;
            }
        }
        if(a[0] > b){
            return leng;
        }else if(a[leng-1] <= b){
            return 0;
        }else{
            if(a[max] <= b){
                return leng-(max+1);
            }
            return leng-(min+1);
        }
    }
    // 1からaまでの数字並べ替え全通り返すやつ
    static List<string> permutation(int a){var list = new List<string>();if(a == 1){list.Add("1");return list;}else{foreach(var k in permutation(a-1)){var ch = k.ToCharArray();for(int i=0;i<=ch.Length;i++){string intemp = "";if(i == 0){intemp += a.ToString();}for(int j=0;j<ch.Length;j++){intemp += ch[j].ToString();if(i == j+1){intemp += a.ToString();}}list.Add(intemp);}}}return list;}
    static void swap(ref int a,ref int b){int temp = a;a= b;b = temp;}
    static void charswap(ref char a,ref char b){char temp = a;a= b;b = temp;}
    static int ncr(int n,int r){r = Min(r,n-r);long nn = 1;for(int i=n-r+1;i<=n;i++){nn = nn*i%mod;}long rr = 1;for(int i=1;i<=r;i++){rr = rr*i%mod;}rr = square((int)rr,mod-2);nn = nn * rr %mod;return (int)nn;}
    // a^b mod
    static int square(int a,int b){string binary = Convert.ToString(b,2);int bileng = binary.Length;long a_power = a;long value = 1;for(int i=bileng-1;i>=0;i--){if(binary[i] == '1'){value = value*a_power%mod;}a_power = a_power*a_power%mod;}return (int)value;}
    static int square2(int a,int b){long output = 1;var list = new List<long>();int sh = 1;long n = a;list.Add(a);while(sh < b){sh *= 2;n = n*n%mod;list.Add(n);}for(int i=list.Count-1;i>=0;i--){if(b > sh){b -= sh;sh /= 2;output = output*list[i]%mod;}}return (int)output;}
    //各種読取
    static string rstr(){ return ReadLine(); }
    static int rint(){ return int.Parse(ReadLine()); }
    static long rlong(){ return long.Parse(ReadLine()); }
    static string[] stra(){ return ReadLine().Split(' '); }
    static char[] chara(){ string[] a=stra();string b="";for(int i=0;i<a.Length;i++){b+=a[i];}return b.ToCharArray();}
    static int[] inta(){ string[] read_str_array = ReadLine().Split(' '); int[] return_int_array = new int[read_str_array.Length]; for(int countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_int_array[countup_i] = int.Parse(read_str_array[countup_i]); } return return_int_array; }
    static int[,] inta2(int num_array,int in_array){ int[,] int_array2 = new int[num_array,in_array]; for(int i=0;i<num_array;i++){ int[] temp_array = inta(); for(int j=0;j<in_array;j++){ int_array2[i,j] = temp_array[j]; } } return int_array2; }
    static long[] longa(){ string[] read_str_array = ReadLine().Split(' '); long[] return_long_array = new long[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_long_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_long_array; }
    static double[] doublea(){ string[] read_str_array = ReadLine().Split(' '); double[] return_double_array = new double[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_double_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_double_array; }
    // -----------------------------
    static long divideup(long divided,long divid){ long temp_divide = divided/divid; if(divided % divid > 0){ temp_divide++; } return temp_divide; }
    static long GCD(long a,long b){ if(a < b){ long temp = a; a = b; b = temp; } if(a % b == 0){ return b; } else{ long temp = b; b = a%b; a = temp; return GCD(a,b); } }
    static long LCM(long a,long b){ return a * b / GCD(a,b); }
}