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 Hw
{
    public static void main (String [] args)
    {
        Scanner in = new Scanner (System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        in.nextLine();
        String s = in.nextLine();
        int length = s.length();
        String l = "";

        for (int i = 0; i < length; i++)
        {
            String a = s.substring(0,i);
            String b = s.substring(length-i,length);
            if (a.equals(b)) {
                l = a;
            }
        }

        int o = l.length();
        String nm = s.substring(0,length-o);
        String fi ="";
        for (int j= 0; j < k; j++)
            fi = fi + nm;
        System.out.println(fi+l);



    }
}