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.*;
public class A
{
      public static void main(String ar[])
      {
       Scanner s=new Scanner(System.in);
       int n=s.nextInt();  int k=s.nextInt();  s.nextLine();
       String S=s.nextLine();
       int t=0;
       for(int i=1;i<n;i++)
       {
         int j=0;   int r=i;
         while(r<n)
         {
               if(S.charAt(r)!=S.charAt(j))
                break;
               if(r==n-1)
                t=i;
                j++;  r++;
         }
         if(t!=0)
          break;
       }
       String T=S.substring(n-t);
       System.out.print(S);
       if(t!=0)
       for(int i=0;i<k-1;i++)
        System.out.print(T);
       else
       for(int i=0;i<k-1;i++)
        System.out.print(S);
      }
}