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.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
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            char[] s = in.nextLine().toCharArray();

            int[] letters;
            int[] letter2val;
            int nletters = 0;
            {
                letter2val = new int[26];
                Arrays.fill(letter2val, -1);
                for (int i = 0; i < s.length; i++) {
                    letter2val[s[i] - 'a'] = 1;
                }
                for (int i = 0; i < letter2val.length; i++) {
                    if (letter2val[i] == 1)
                        letter2val[i] = nletters++;
                }
                letters = new int[nletters];
                int pos = 0;
                for (int i = 0; i < letter2val.length; i++) {
                    if (letter2val[i] > -1)
                        letters[pos++] = i;
                }
            }

            if (k > n) {
                out.print(s);
                for (int i = 0; i < k - s.length; i++) {
                    out.print((char) (letters[0] + 'a'));
                }
                out.println();
                return;
            }

            int[] word = new int[k];
            for (int i = 0; i < k; i++) {
                word[i] = letter2val[s[i] - 'a'];
            }

            for (int i = k - 1; i >= 0; i--) {
                if (word[i] + 1 < nletters) {
                    word[i]++;
                    break;
                } else {
                    word[i] = 0;
                }
            }

            for (int i = 0; i < word.length; i++) {
                out.print((char) (letters[word[i]] + 'a'));
            }
            out.println();
        }

    }

    static class InputReader {
        StringTokenizer st;
        BufferedReader br;

        public InputReader(InputStream is) {
            BufferedReader br = new BufferedReader(new InputStreamReader(is));
            this.br = br;
        }

        public String next() {
            if (st == null || !st.hasMoreTokens()) {
                String nextLine = null;
                try {
                    nextLine = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (nextLine == null)
                    return null;
                st = new StringTokenizer(nextLine);
            }
            return st.nextToken();
        }

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

        public String nextLine() {
            String str = null;
            try {
                str = br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return str;
        }

    }
}

