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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author NMouad21
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FReader in = new FReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        AManyEqualSubstrings solver = new AManyEqualSubstrings();
        solver.solve(1, in, out);
        out.close();
    }

    static class AManyEqualSubstrings {
        public void solve(int testNumber, FReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            String t = in.next();
            String s = t;

            while (--k > 0) {
                int idx = 0;
                for (int i = t.length() - 1; i >= 0; --i) {
                    if (can(s, t, i)) {
                        idx = i;
                        break;
                    }
                }

                s += t.substring(idx);
            }

            out.print(s);
        }

        private boolean can(String s, String t, int i) {
            for (int j = 0; j < i; ++j) {
                if (t.charAt(j) != s.charAt(s.length() - i + j)) {
                    return false;
                }
            }
            return true;
        }

    }

    static class FReader {
        private BufferedReader r;
        private String line;
        private StringTokenizer st;
        private String token;

        public FReader() {
            this(System.in);
        }

        public FReader(InputStream i) {
            r = new BufferedReader(new InputStreamReader(i));
        }

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

        public String next() {
            return nextToken();
        }

        private String peekToken() {
            if (token == null)
                try {
                    while (st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if (line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch (IOException e) {
                }
            return token;
        }

        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }

    }
}