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.Arrays;
import java.util.Scanner;

public class Main {


    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int length = scanner.nextInt();
        int subStrTotal = scanner.nextInt();
        String str = scanner.next();

        int flag = 0;
        int[] arr = new int[length];
        Arrays.fill(arr, 0);
        int lastPos = 0;
        int i = 1;
        while(i < length) {
            if (str.charAt(i) == str.charAt(lastPos)) {
                lastPos++;
                arr[i] = lastPos;
                i++;
            } else if (lastPos != 0) {
                lastPos = arr[lastPos - 1];
            } else {
                i++;
            }
        }

        flag = arr[length - 1];
        String strPrefixSuff = str.substring(flag);
        StringBuilder res = new StringBuilder(str);
        for (int j = 1; j < subStrTotal; j++) {
            res.append(strPrefixSuff);
        }

        System.out.println(res.toString());
    }
}