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 A {

	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int t = scan.nextInt();
		int k = scan.nextInt();
		scan.nextLine();
		String s = scan.nextLine().trim();
		String finalAns = s;
		String biggestStart = "";
		int startLenght = 0;
		String currentTest = "";
		for (int j = 0; j < s.length(); j++) {
			String test = s.substring(j, t);
			if ((s + test).endsWith(s)) {
				if (test.length() < finalAns.length()) {
					finalAns = test;
				}
			}
		}
		String answer = s;
		for (int i = 1; i < k; i++) {
			answer = answer + finalAns;
		}
		System.out.println(answer);
	}

}