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 Main {
    public static String res(String str1) {
        String tmp = "";
        char[] s1 = str1.toCharArray();
        int[] next = next(s1);
        for(int i = next[str1.length()];i < str1.length();i++)
            tmp += str1.charAt(i);
        return str1 + tmp;
    }
    public static int[] next(char[] s1) {
        if(s1.length == 0)
            return new int[] {-1};
        int[] next = new int[s1.length + 1];
        next[0] = -1;
        next[1] = 0;
        int cn = 0;
        int i = 2;
        while(i <= s1.length) {
            if(s1[i - 1] == s1[cn])
                next[i++] = ++cn;
            else if(cn > 0)
                cn = next[cn];
            else
                next[i++] = 0;
        }
        return next;
    }
    public static void main(String[] args) {
    	Scanner cin = new Scanner(System.in);
    	int n = cin.nextInt();
    	int m = cin.nextInt();
    	String str = cin.next();
    	for(int i = 1;i < m;i++)
    		str = res(str);
    	System.out.println(str);
    }
}