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.*;
import java.util.*;
import java.math.*;
import static java.lang.System.out;

public class CF1029A
{
    public static void main(String[] args) throws IOException
    {
        //BufferedReader f = new BufferedReader(new FileReader("/Users/spencersharp/Desktop/input.txt"));
        
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(new BufferedOutputStream(System.out));
        
        String output = ""; //Write all output to this string

        //Code here
        StringTokenizer st = new StringTokenizer(f.readLine());
        int len = Integer.parseInt(st.nextToken());
        int numSubstrings = Integer.parseInt(st.nextToken());
        
        output += f.readLine();
        String input = output;
        
        for(int i = 0; i < numSubstrings - 1; i++)
        {
            String toAdd = input;
            for(int j = 1; j < len; j++)
            {
                boolean possible = true;
                for(int k = 0; k < len - j; k++)
                {
                    //if(j == 5)
                    //    out.println(input.charAt(j + k) + " " + input.charAt(k));
                    if(input.charAt(j + k) != input.charAt(k))
                    {
                        possible = false;
                        break;
                    }
                }
                
                if(possible)
                {
                    //out.println();
                    toAdd = input.substring(len-j);
                    break;
                }
            }
            output += toAdd;
        }
        
        
        //Code here

        //out.println(output);
        
        writer.println(output);
        writer.close();
        System.exit(0);
        
    }
}