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) {
        TaskA Solver = new TaskA();
        Solver.Solve();
    }
    private static class TaskA {
        private void Solve() {
            Scanner in = new Scanner(System.in);
            int n = in.nextInt();
            int k = in.nextInt();
            String S = in.next();
            int len = S.length();
            StringBuilder ans = new StringBuilder(S);
            for (int i = 1; i < k; i++) {
                int l = ans.length();
                for (int j = l - len; j <= l; j++) {
                    StringBuilder newAns = new StringBuilder(ans.substring(0, j));
                    newAns.append(S);
                    if (AmountSubstring(newAns, S) == i + 1) {
                        ans = newAns;
                        break;
                    }
                }
            }
            System.out.println(ans);
        }
        private int AmountSubstring(StringBuilder S, String sub) {
            StringBuilder remS = new StringBuilder(S);
            int amount = 0;
            while (true) {
                int indx = remS.indexOf(sub);
                if (indx == -1)
                    break;
                else {
                    remS.replace(indx, indx + 1, "!");
                    amount++;
                }
            }
            return amount;
        }
    }
}