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.Scanner;

public class Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		String str=sc.next();
		StringBuilder sb=new StringBuilder();
		int count=0;
		for(int i=0;i<n;i++)
		{
			int c=0;
			int flag=1;
			for(int j=i+1,z=0;j<n&&flag==1;j++,z++)
			{
				if(str.charAt(j)==str.charAt(z))
				{
					c++;
				}
				else
				{
					flag=0;
				}
			}
			if(flag==1 && c>count)
			{
				count=c;
			}
		}
		if(count>0 && k>0)
		{
			sb.append(str);
			k--;
			while(k>0)
			{
				sb.append(str.substring(count,str.length()));
				k--;
			}
		}
		else
		{
			while(k>0)
			{
				sb.append(str);
				k--;
			}
		}
		System.out.println(sb.toString());
	}

}