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.*;
import java.io.*;

public class Main {
	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		StringBuilder sb = new StringBuilder();
		
		StringTokenizer st = new StringTokenizer(in.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		
		String t = in.readLine();
		int idx = 0;
		for(int i=1; i<=n; i++) {
			String temp = t.substring(0, n-i);
			String c2 = t.substring(i);
			if(temp.equals(c2)) {
				idx = i;
				break;
			}
		}
		String sub = t.substring(n-idx);
		sb.append(t);
		for(int i=1; i<k; i++)
			sb.append(sub);
		System.out.println(sb);
	}
	
}