And where the are the phone numbers?

You are given a string s consisting of lowercase English letters and an integer k. Find the lexicographically smallest string t of length k, such that its set of letters is a subset of the set of letters of s and s is lexicographically smaller than t.

It's guaranteed that the answer exists.

Note that the set of letters is a set, not a multiset. For example, the set of letters of abadaba is {a, b, d}.

String p is lexicographically smaller than string q, if p is a prefix of q, is not equal to q or there exists i, such that pi < qi and for all j < i it is satisfied that pj = qj. For example, abc is lexicographically smaller than abcd , abd is lexicographically smaller than abec, afa is not lexicographically smaller than ab and a is not lexicographically smaller than a.

Input

The first line of input contains two space separated integers n and k (1 ≤ n, k ≤ 100 000) — the length of s and the required length of t.

The second line of input contains the string s consisting of n lowercase English letters.

Output

Output the string t conforming to the requirements above.

It's guaranteed that the answer exists.

Examples

Input

3 3
abc


Output

aca


Input

3 2
abc


Output

ac


Input

3 3
ayy


Output

yaa


Input

2 3
ba


Output

baa

Note

In the first example the list of strings t of length 3, such that the set of letters of t is a subset of letters of s is as follows: aaa, aab, aac, aba, abb, abc, aca, acb, .... Among them, those are lexicographically greater than abc: aca, acb, .... Out of those the lexicographically smallest is aca.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class TaskC {
        boolean[] mrk;

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            mrk = new boolean[30];
            Arrays.fill(mrk, false);
            String s = in.nextLine();

            for (int i = 0; i < n; i++) {
                mrk[s.charAt(i) - 'a'] = true;
            }
            int p = Math.min(n, k);
            StringBuilder sub = new StringBuilder(s.substring(0, p));
            //out.println(sub);

            if (k > n) {
                int i = findGreater(-1);
                for (int j = 0; j < k - n; j++) sub.append((char) ('a' + i));
                out.println(sub);
            } else if (n >= k) {
                StringBuilder ans = new StringBuilder();
                for (int i = k - 1; i >= 0; i--) {
                    int x = sub.charAt(i) - 'a';
                    int y = findGreater(x);
                    if (y != -1) {
                        ans.append(sub.substring(0, i));
                        ans.append((char) (y + 'a'));
                        break;
                    }
                }
                int d = k - ans.length();
                int z = findGreater(-1);
                for (int i = 0; i < d; i++) ans.append((char) ('a' + z));
                out.println(ans);
            }
        }

        private int findGreater(int k) {
            for (int i = 0; i < 30; i++) {
                if (i > k && mrk[i]) return i;
            }
            return -1;
        }

    }

    static class FastScanner {
        private BufferedReader bufferedReader;
        private StringTokenizer stringTokenizer;

        public FastScanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        }

        public String next() {
            if (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

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

        public String nextLine() {
            String ret = "";
            try {
                ret = bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return ret;
        }

    }
}

