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.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Scanner;

public class codeforces {

	public static void main(String[] args)throws IOException 
	{
	  Scanner in = new Scanner(System.in);	
	  int n=in.nextInt();
	  int k=in.nextInt();
	  String s1=in.next();
	  int i=0;
	  
	  int p=0;
	 for(i=0;i<n;i++)
	 {
		 if(s1.endsWith(s1.substring(0,i)))
		 {
			 p=i;
		 }
	 }
	 
	 for(i=0;i<k-1;i++)
	 {
		 System.out.print(s1.substring(0,n-p));
	 }
	 System.out.println(s1);
	 
	  
	  
	  
	  
    }	
	}