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




public class A {

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        new A();
    }

    A()throws IOException{
        solve();
    }

    void solve()throws IOException {
        int n = Reader.nextInt();
        int k = Reader.nextInt();
        String x = Reader.next();
        StringBuilder out = new StringBuilder();
        out.append(x);
        k--;
        int last = 1;
        while(k > 0){
            int prev = k;
            for(int i = last; i < out.length(); i++){
                if(out.toString().substring(i,out.length()).equals(x.substring(0, out.length()-i))){last = i+1; out.append(x.substring(out.length()-i, n)); k--; break;}
            }
            if(k == prev){last = last + n ; out.append(x); k--;}
        }
        System.out.println(out.toString());
    }

}



class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;
    /** call this method to initialize reader for InputStream */

    static void init(InputStream input) {
        reader = new BufferedReader(new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");

    }

    static String nextToken() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {

                tokenizer = new StringTokenizer(reader.readLine());

            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    static String next() throws IOException {

        while ( ! tokenizer.hasMoreTokens() ) {

            tokenizer = new StringTokenizer(

                    reader.readLine() );

        }
        return tokenizer.nextToken();

    }

    static int nextInt() throws IOException {

        return Integer.parseInt( next() );

    }

    static double nextDouble() throws IOException {

        return Double.parseDouble( next() );

    }

    static long nextLong() {

        return Long.parseLong(nextToken());
    }
}