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.*;
public class Main{
    


public static void main(String[] args) {

		// we will get the first char and check how many characters from the first one are equals other characters 
		// starting from some position till the end, to avoid these characters while getting the result
		Scanner input = new Scanner(System.in);

		int n, k;
		String t;
		n = input.nextInt();
		k = input.nextInt();
		input.nextLine();
		t = input.nextLine();
		int index = 0;
		for (int i = 1; i < t.length(); i++) {

			if (t.charAt(0) == t.charAt(i)) {
				int numberOfMatchedCharacters = t.length() - i;

				if (t.substring(0, numberOfMatchedCharacters).equals(t.substring(i))) {

					index = numberOfMatchedCharacters;
					break;
				}

			}
		}
		String s=t;

		for (int i = 0; i < k-1; i++) {
			s += t.substring(index);
		}

		System.out.println(s);
}
}