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.io.*;
import java.util.*;

public class ManyEqualSubstrings {
	
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		String s = br.readLine();
		StringBuilder ans = new StringBuilder();
		int idx=0;
		for (int i=0;i<s.length();i++) {
			if ((s.substring(0, i).equals(s.substring(s.length()-i)))) {
				idx =i;
			}
		}
		for (int i=0;i<idx;i++) {
			pw.print(s.charAt(i));
		}
		for (int i=idx;i<s.length();i++) {
			ans.append(s.charAt(i));
		}
		for (int i=0;i<k;i++) {
			pw.print(ans);
		}
		pw.close();
		pw.flush();
	}
}