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) {

        int n, k;
        String t;

        Scanner in = new Scanner(System.in);

        n = in.nextInt();
        k = in.nextInt();

        t = in.next();

        //System.out.println(t);

        // find MAX border:
        int maxBord = 0;

        for (int i = n-1; i >= 1; i--) {
            // [0, i)
            String b1 = t.substring(0, i);
            String b2 = t.substring(n - i);

            if (b1.compareTo(b2) == 0) {
                assert b1.length() == i;

                maxBord = i;
                break;
            }
        }

        String s1 = t.substring(maxBord);

        StringBuilder sb = new StringBuilder();

        sb.append(t);

        for (int i = 1; i < k; i++) {
            sb.append(s1);
        }

        System.out.println(sb);





    }
}