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 edu_1029_A
{
    public static void main(String args[])
    {
        Scanner ob=new Scanner(System.in);
        int n=ob.nextInt();
        int k=ob.nextInt();
        String s=ob.next();
        int ind=0;
        int lenmax=0;
        for(int i=n-1;i>=0;i--)
        {
            String s1=s.substring(0,i);
            String s2=s.substring(n-i,n);
            //System.out.println(s1+" "+s2);
            if(s1.equals(s2))
            {
                //System.out.println(s1+" "+s2);
                lenmax=i;
                break;
            }
        }
        String cp=s.substring(lenmax,n);
        System.out.print(s);
        for(int i=1;i<k;i++)
        {
            System.out.print(cp);
        }
    }
}