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 Solution {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        String s = sc.next();
        
        int maxPrefix=0;
        for(int len = 1; len<n; len++) {
            boolean good = true;
            for(int i = 0; i<len; i++) {
                if(s.charAt(i)!=s.charAt(n-len+i)) {
                    good=false;
                    break;
                }
            }
            if(good)
                maxPrefix=len;
        }
        
        String postfix = s.substring(maxPrefix);
        StringBuilder result = new StringBuilder(s);
        for(int i = 0; i<k-1; i++) {
            result.append(postfix);
        }
        System.out.println(result.toString());
    }
}