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.Scanner;

public class one {
    public static void main(String args[])
    {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt(), k = scan.nextInt();
        String s = scan.next();
        StringBuilder output = new StringBuilder();
        int length = 0;

        output.append(s);
        for (int i = 1; i < n; i++){
            if (s.startsWith(s.substring(s.length() - i))) {
                length = i;
            }
        }
        k--;

        while (k-- > 0) {
            output.append(s.substring(length));
        }

        System.out.println(output);

    }
}