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.*;
/**
 * Write a description of ProblemA here.
 * 
 * @author (your name) 
 * @version (a version number or a date)
 */
public class ProblemA {
    public String substring;
    public int substringLenght;
    public int numOfSubstrings;
    
    public ProblemA(){
        substring = new String();
    }
    
    public int addSubstring(String wholeString)
    {
            int i=1;
            int breaker = substringLenght-1; //2
            for(i =1; i < substringLenght; i++)
            {
                breaker--; //1  //ba //ab    //0 //a //1
                if ( substring.substring(i,substringLenght).equals(substring.substring(0,substringLenght-i)) )
                { 
                      return breaker+1;
                }
             
            }  
            return 0;
    }
    public static void main(String[] args) {
        ProblemA solve = new ProblemA();
        Scanner sc = new Scanner(System.in);
        solve.substringLenght = sc.nextInt();
        solve.numOfSubstrings = sc.nextInt();
        solve.substring=sc.next();
        String wholeString = solve.substring;
        int breaker;
        //make the substring
        breaker = solve.addSubstring(wholeString);

        for (int i=1; i < solve.numOfSubstrings; i++)
        {
                wholeString= wholeString + solve.substring.substring(breaker,(solve.substringLenght));
        }


        //check the wholestring
        //abaabaabaabaaba
        //System.out.println(breaker);
        System.out.println(wholeString);
    }

}