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.io.*;
import java.util.*;


public class Main {






    public static void main(String[] args) throws FileNotFoundException {
        Reader rd = new Reader(System.in);
        int n = rd.nextInt();
        int k = rd.nextInt();
        String inp = rd.next();
        int maxPreSuff =0;
        //System.out.println(inp);
        Integer [] lps  = new Integer[n];
        Arrays.fill(lps,0);
        Integer lastLps = 0;
        Integer i  = 1;
        while(i<n){
            if(inp.charAt(i)==inp.charAt(lastLps)){
                lastLps++;
                lps[i]=lastLps;
                i++;
            }else if(lastLps!=0){
                lastLps = lps[lastLps-1];
            }else{
                i++;
            }
        }

        maxPreSuff = lps[n-1];
        String toAppend = inp.substring(maxPreSuff);
        StringBuilder sb = new StringBuilder(inp);

        while(k-- !=1 ){
            sb.append(toAppend);
        }
        System.out.println(sb.toString());



    }

    public static class Reader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public Reader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

    }



}