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:
//package codeforce;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Tester {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();
		int k=s.nextInt();
		String st=s.next();
		int len=st.length();
		int lps[]=new int[n];
		compute(lps,st);
		String tmp=st.substring(lps[len-1], len);
		String ans=st;
		for(int i=1;i<=k-1;i++)
			ans+=tmp;
		System.out.println(ans);
		

	}
	public static void compute(int lps[],String st)
	{
		int i=1;
		int len=0;
		while(i<st.length())
		{
			if(st.charAt(len)==st.charAt(i))
			{
				len++;
				lps[i]=len;
				i++;
			}
			else
			{
				if(len>0)
				{
					len=lps[len-1];
				}
				else
				{
					lps[i]=0;
					i++;
				}
			}
		}
	}

}
class FastReader
{
	BufferedReader br;
	StringTokenizer st;

	public FastReader()
	{
		br = new BufferedReader(new
				InputStreamReader(System.in));
	}

	String next()
	{
		while (st == null || !st.hasMoreElements())
		{
			try
			{
				st = new StringTokenizer(br.readLine());
			}
			catch (IOException  e)
			{
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}

	int nextInt()
	{
		return Integer.parseInt(next());
	}

	long nextLong()
	{
		return Long.parseLong(next());
	}

	double nextDouble()
	{
		return Double.parseDouble(next());
	}

	String nextLine()
	{
		String str = "";
		try
		{
			str = br.readLine();
		}
		catch (IOException e)
		{
			e.printStackTrace();
		}
		return str;
	}
}