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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {
    /**********************************************************************************************
     *                                            DEBUG                                           *
     **********************************************************************************************/
    private final static boolean DEBUG = false;
    private final static String[] DEBUG_INPUT = {
//            "4 3\n" +
//                    "acdb",
            "3 3\n" +
                    "abc",
            "3 2\n" +
                    "abc",
            "3 3\n" +
                    "ayy",
            "2 3\n" +
                    "ba"
    };



    /**********************************************************************************************
     *                                             MAIN                                           *
     **********************************************************************************************/
    private static class Solver {
        public void solve(Reader in, PrintWriter out) throws IOException {
            int n = in.nextInt();
            int k = in.nextInt();
            String s = in.nextWord();

            boolean[] check = new boolean[26];
            int count = 0;
            for (int i = 0; i < n; i++) {
                int idx = s.charAt(i) - 'a';
                if (!check[idx]) {
                    check[idx] = true;
                    count++;
                }
            }
            char[] set = new char[count];
            for (int i = 0, j = 0; i < count; i++) {
                while (!check[j]) j++;
                set[i] = (char) ('a' + j);
                j++;
            }

            if (k > n) {
                StringBuilder sb = new StringBuilder(s);
                for (int i = n; i < k; i++) sb.append(set[0]);
                out.println(sb.toString());
            } else {
                StringBuilder sb = new StringBuilder(s.substring(0, k));
                int i = k-1;
                while (i >= 0) {
                    char c = sb.charAt(i);
                    int idx = Arrays.binarySearch(set, (char)(c + 1));
                    if (idx < 0) idx = ~idx;
                    if (idx == set.length) {
                        while (sb.charAt(i) == c) i--;
                    } else {
                        sb.setCharAt(i, set[idx]);
                        for (int j = i + 1; j < k; j++) sb.setCharAt(j, set[0]);
                        break;
                    }
                }
                out.println(sb.toString());
            }
        }
    }



    /**********************************************************************************************
     *                                           TEMPLATE                                         *
     **********************************************************************************************/
    public static void main(String[] args) throws IOException {
        PrintWriter out = null;
        Reader in;
        if (DEBUG) {
            for (String s : DEBUG_INPUT) {
                in = new Reader(new ByteArrayInputStream(s.getBytes()));
                out = new PrintWriter(System.out);
                out.println("===>>> INPUT");
                out.println(s + "\n\n");
                out.println("===>>> OUTPUT");
                long start = System.currentTimeMillis();
                new Solver().solve(in, out);
                long end = System.currentTimeMillis();
                out.println("\n");
                out.println("===========");
                out.println("Took: " + (end - start) + "ms");
                out.println("====================================================================");
                out.println();
                out.println();
                out.flush();
            }
        } else {
            in = new Reader(System.in);
            out = new PrintWriter(System.out);
            new Solver().solve(in, out);
        }
        if (out != null) out.flush();
    }

    /** Reader **/
    private static class Reader {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public Reader(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }

        private String nextWord() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
            return tokenizer.nextToken();
        }

        private int nextInt() throws IOException {
            return Integer.parseInt(nextWord());
        }

        private long nextLong() throws IOException {
            return Long.parseLong(nextWord());
        }

        private double nextDouble() throws IOException {
            return Double.parseDouble(nextWord());
        }
    }
}
