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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class TestClass {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] s = br.readLine().split(" ");
		int n = Integer.parseInt(s[0]);
		int k = Integer.parseInt(s[1]);
		String ip = br.readLine();
		
		int cnt = 1;
		int pos = 1;
		StringBuffer ans = new StringBuffer();
		ans.append(ip);
		
		while(cnt < k){
			if(pos >= ans.length()){
				ans.append(ip);
				++cnt;
			}
			else{
				boolean ok = true;
				int len = 0;
				for(int i = 0 ; i < ip.length(); i++){
					if(pos + i >= ans.length()) break;
					++len;
					if(ans.charAt(pos + i) != ip.charAt(i))
						ok = false;
				}
				if(ok){
					ans.append(ip.substring(len , ip.length()));
					++cnt;
				}
			}
			++pos;
		}
		System.out.println(ans);
	}
}