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 EqSubstring {
    static int prefixSuffix(String s) {
        for (int len = s.length() - 1; len > 0; len--) {
            boolean isPrefSuff = true;
            for (int i = 0; i < len; i++) {
                isPrefSuff &= (s.charAt(i) == s.charAt(s.length() - len + i));
            }
            if (isPrefSuff) return len;
        }
        return 0;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        String s = scanner.next();
        int prefSuff = prefixSuffix(s);
        StringBuilder stringBuilder = new StringBuilder();
        stringBuilder.append(s);
        for (int i = 0; i < k - 1; i++) {
            for (int j = prefSuff; j <s.length(); j++) {
                stringBuilder.append(s.charAt(j));
            }
        }
        System.out.println(stringBuilder.toString());
    }
}