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 A1029 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        in.nextInt();
        int K = in.nextInt();
        String S = in.next();
        StringBuilder result = new StringBuilder();
        result.append(S);
        for (int k=1; k<K; k++) {
            for (int i=S.length()-1; i>=0; i--) {
                String s = S.substring(0, i);
                if (result.toString().endsWith(s)) {
                    result.append(S.substring(i));
                    break;
                }
            }
        }
        System.out.println(result);
    }

}