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 A {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] ss = br.readLine().split("\\s+");
		int n = Integer.valueOf(ss[0]);
		int k = Integer.valueOf(ss[1]);
		String t = br.readLine();
		int index = 0;
		for(int i=1, j=t.length()-1; i < t.length(); i++, j--) {
			String s1 = t.substring(i);
			String s2 = t.substring(0, j);
			if (s1.equals(s2)) {
				index = j;
				break;
			}
		}
		int instances = 1;
		StringBuilder sb = new StringBuilder(t);
		String subs = t.substring(index);
		while(instances < k) {
			sb.append(subs);
			instances++;
		}
		System.out.println(sb.toString());
	}
}