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 A1029 {

	public static void main(String[] args) {
		
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int k = s.nextInt();
		String word = s.next();
		int overlap = 0;
		int worked = 0;
		while (overlap + 1 < word.length()) {
			if (check(word, overlap +1)) {
				worked = overlap + 1;
			}
			overlap++;
		}
		String next = word.substring(worked);
		String out = word;
		for (int i = 1; i < k; i++) out += next;
		System.out.println(out);
		
	}
	
	public static boolean check(String word, int overlap) {
		
		for (int i = word.length() - overlap; i < word.length(); i++) {
			if (word.charAt(i) != word.charAt(i - word.length() + overlap)) {
				return false;
			}
		}
		return true;
		
	}
	
}