Problem: You are given a string t consisting of n lowercase Latin letters and an integer number k.

Let's define a substring of some string s with indices from l to r as s[l ... r].

Your task is to construct such string s of minimum possible length that there are exactly k positions i such that s[i ... i + n - 1] = t. In other words, your task is to construct such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 50) — the length of the string t and the number of substrings.

The second line of the input contains the string t consisting of exactly n lowercase Latin letters.

Output

Print such string s of minimum possible length that there are exactly k substrings of s equal to t.

It is guaranteed that the answer is always unique.

Examples

Input

3 4
aba


Output

ababababa


Input

3 2
cat


Output

catcat

Solution (in JAVA):

Solution:
 import java.util.Scanner;
public class manyEqualSubstrings
{
    public static Scanner scan=new Scanner(System.in);
    public static void main(String args[])
    {
        int n,m;
        String resp="",pal;
        n=scan.nextInt();
        m=scan.nextInt();
        pal=scan.next();
        resp=manyEqual(n,m,pal);
        System.out.println(resp);
    }
    
   static public String manyEqual(int n, int m, String pal)
    {
        String resp=pal;
        boolean bandera=false;
        for(int i=1;i<m;i++)
        {
               for(int k=0;k<resp.length()-1;k++)
               {
                   if(resp.substring((resp.length()-(pal.length()-1))+k).equals(pal.substring(0,pal.length()-(k+1))))
                   { 
                       resp=resp+pal.substring(pal.substring(0,pal.length()-(k+1)).length(),pal.length());
                       k=resp.length();
                       bandera=true;
                   }
                   
           }
           if(bandera==false)
            resp=resp+pal;
        }
        return resp;
    }
}