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.BufferedReader;
import java.io.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;

import static java.lang.Math.*;

public class PhoneNumbers implements Closeable {

    private InputReader in = new InputReader(System.in);
    private PrintWriter out = new PrintWriter(System.out);

    public void solve() {
        int n = in.ni(), k = in.ni();
        char[] x = in.next().toCharArray();
        boolean[] set = new boolean[26];
        for (int i = 0; i < n; i++) {
            set[x[i] - 'a'] = true;
        }
        List<Character> letters = new ArrayList<>();
        for (int i = 0; i < 26; i++) {
            if (set[i]) {
                letters.add((char) ('a' + i));
            }
        }
        int count = letters.size();
        char[] result = new char[k];
        if (k > n) {
            for (int i = 0; i < k; i++) {
                if (i < n) {
                    out.print(x[i]);
                } else {
                    out.print(letters.get(0));
                }
            }
        } else {
            int idx = -1;
            char worst = letters.get(count - 1);
            for (int i = min(n - 1, k - 1); i >= 0; i--) {
                if (x[i] < worst) {
                    idx = i;
                    break;
                }
            }
            char replace = '?';
            for (char c : letters) {
                if (c > x[idx]) {
                    replace = c;
                    break;
                }
            }
            result[idx] = replace;
            for (int i = 0; i < idx; i++) {
                result[i] = x[i];
            }
            for (int i = idx + 1; i < k; i++) {
                result[i] = letters.get(0);
            }
            for (char c : result) {
                out.print(c);
            }
        }
    }

    @Override
    public void close() throws IOException {
        in.close();
        out.close();
    }

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

        public InputReader(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 ni() {
            return Integer.parseInt(next());
        }

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

        public void close() throws IOException {
            reader.close();
        }
    }

    public static void main(String[] args) throws IOException {
        try (PhoneNumbers instance = new PhoneNumbers()) {
            instance.solve();
        }
    }
}
