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.*;

public class test {

  public static void main(String[] args) {
    Scanner in = new Scanner(System.in);
    int n = in.nextInt();
    int k = in.nextInt();
    String t = in.next();
    
    StringBuilder result = new StringBuilder(t);
    t = getStr(t);
    for (int i=1; i< k; i++) {
      result.append(t);
    }
    System.out.print(result.toString());    	
  }
  
  private static String getStr(String str){
    int len = str.length();
    if (len == 1) {
      return str;
    }
    for (int z = str.length() - 1; z > 0; z--) {
      if (str.substring(str.length() - z , str.length()).equals(str.substring(0, z))) {
      	return str.substring(z , str.length());
      }
    }
    return str;
  }
}