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[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), k = in.nextInt();
        String s = in.next(), min = min(s);
        
        for (int i = 0; i < k-1; i++)
            s += min;
            
        System.out.println(s);
        in.close();
    }
    
    public static String min(String s)
    {
        for (int i = s.length()-1; i > 0; i--)
            if (s.substring(0, i).equals(s.substring(s.length()-i)))
                return s.substring(i);
 
        return s;
    }
}