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;
import java.lang.Math.*;

public class ManyEqualSubstrings {

	private static String appendOnce (String orig, String sub, int subLength) {
		int origLength = orig.length();
		if(subLength == 1) {
			return orig.concat(sub);
		}
		int startIndex = -1;
		for(int tryIndex = Math.max(0, origLength - subLength + 1); tryIndex < origLength; tryIndex++) {
			Boolean match = true;
			for(int index = 0; tryIndex+index < origLength; index++) {
				if(sub.charAt(index) != orig.charAt(tryIndex+index))
					match = false;
			}
			if(match) {
				startIndex = tryIndex;
				break;
			}
		}
		if(startIndex != -1) {
			int alreadyIn = origLength - startIndex;
			return orig.concat(sub.substring(alreadyIn));
		} else {
			return orig.concat(sub);
		}
	}

	public static String appendSub (String orig, String sub, int length, int times) {
		String ans = orig;
		for(int count = 0; count < times; count++) {
			ans = appendOnce(ans, sub, length);
		}
		return ans;
	}

	public static void main (String[] args) {

		Scanner reader = new Scanner(System.in);

		int length = reader.nextInt();
		int times = reader.nextInt();
		String sub = reader.next();

		String ans = appendSub( "", sub, length, times);
		System.out.println(ans);
	}
}