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 boolean isSingleLetter(String s) {
        for(int i = 1; i < s.length(); i++) {
            if(s.charAt(i) != s.charAt(0))
                return false;
        }
        return true;
    }

    public static void solve(String s, int k) {
        if(isSingleLetter(s)) {
            for(int i = 0; i < s.length() + k - 1; i++) {
                System.out.print(s.charAt(0));
            }
            System.out.println();
            return;
        }

        int start = 1;
        loop: for(; start < s.length(); start++) {
            for(int i = 0; i < s.length() - start; i++) {
                if(s.charAt(i) != s.charAt(start + i)) {
                    continue loop;
                }
            }
            break;
        }

        StringBuffer sb = new StringBuffer();
        sb.append(s);
        String sbstr = s.substring(s.length() - start, s.length());
        for(int i = 0; i < k - 1; i++) {
            sb.append(sbstr);
        }
        System.out.println(sb);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        String str = sc.next();

        solve(str, k);
    }

}