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 Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int n = in.nextInt();
        int k = in.nextInt();
        String t = in.next();

        int i = 0;
        int l = -1;
        for (; i < n - 1; i++) {
            String s1 = t.substring(0, i + 1);
            String s2 = t.substring(n - i - 1);

            if (s1.equals(s2)) l = i;
        }

        if ( l == -1) {
            for (int j = 0; j < k; j++)
                System.out.print(t);

        } else {

            System.out.print(t);
            for (int j = 1; j < k; j++) {
                System.out.print(t.substring(l + 1));
            }
        }

    }
}