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 ManyEqualSubstrings {
	public static void main(String [] args) throws IOException {
		Scanner scan = new Scanner(System.in);
		
		int n = Integer.parseInt(scan.next());
		int k = Integer.parseInt(scan.next());
		String tt = scan.next();
		char[] t = tt.toCharArray();
		int index = 0;
		for(int start = 1; start<n; start++) {
			boolean found = false;
			for(int i = start; i<n; i++) {
				if(t[i] != t[i-start])
					break;
				if(i==n-1)
					found = true;
			}
			if(found) {
				index = n-start;
				break;
			}
		}
		StringBuilder s = new StringBuilder(60);
		for(int i = index; i<n; i++) {
			s.append(t[i]);
		}
		StringBuilder sb = new StringBuilder(3000);
		sb.append(tt);
		for(int i = 0; i<k-1; i++)
			sb.append(s);
		System.out.println(sb);
		scan.close();
	}
}