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.*;

import static java.lang.Math.copySign;
import static java.lang.Math.max;
import static java.lang.Math.min;


public class Main {
    BufferedReader br;
    StringTokenizer in;
    PrintWriter pw;
    Random r;
    int INF = (int) 1e9;
    long LNF = (long) 1e18;
    long mod = (long) (1e9 + 7);
    int pp = 27;
    // you shall not hack!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    //        /*\
    //       ///          /^\
    //      ///    ~~~~  (___)
    //     ///   ~~~~~~~~  \\__
    //   _/_/_  ~/ .& . \~  \\ \
    //  [____] ~|  (__)  |~/ \\/
    //  /_/\  \~|~~~~~~~~~~  /\\
    //      \   ~~~~~~~~~~ _/ \\
    //       \ _    ~~   _/\   \\
    //      /  |        /   \   \\
    //     |  /        |     \   \\
    //    /  /   ___   |      \
    //   /___|  | __|  |_______\
    //      _|  |   |  |_
    //     |____|   |____|
    //       P.S this is omnipotent Gandalf

    int n;

    void solve() throws IOException {
        int n = nextInt();
        int k = nextInt();
        String s = nextToken();
        int ss[] = new int[n];
        TreeSet<Integer> m = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            m.add(s.charAt(i) - 'a');
            ss[i] = s.charAt(i) - 'a';
        }
        if (k <= n) {
            for (int i = k - 1; i >= 0; i--) {
                if (ss[i] == m.last()) {
                } else {
                    pw.print(s.substring(0, i));
                    pw.print((char)(m.higher(ss[i]) + 'a'));

                    char f = (char) (m.first() + 'a');
                    for (int j = i + 1; j < k; j++) {
                        pw.print(f);
                    }
                    return;
                }
            }
        } else {
            pw.print(s);
            char f = (char) (m.first() + 'a');
            for (int i = n; i < k; i++) {
                pw.print(f);
            }
        }

    }

    class point {
        int x;
        int y;

        public point() throws IOException {
            x = nextInt();
            y = nextInt();
        }

        public point(int xx, int yy) {
            x = xx;
            y = yy;
        }
    }

    //***************************************
    class road implements Comparable<road> {
        int to;
        boolean rev;

        public road(int tto) {
            to = tto;
            rev = false;
        }

        @Override
        public int compareTo(road o) {
            return to - o.to;

        }
    }

    String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

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

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

    public void gener() throws IOException {
        pw = new PrintWriter(new FileWriter("input.txt"));
        int n = r.nextInt(5) + 2;
    }

    public void run() throws IOException {
        r = new Random(5);
//        for (int i = 0; i < 100; i++) {
//            gener();
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new OutputStreamWriter(System.out));
//        br = new BufferedReader(new FileReader("input.txt"));
//        pw = new PrintWriter(new FileWriter("output.txt"));
//        br = new BufferedReader(new FileReader("pixels.in"));
//        pw = new PrintWriter(new FileWriter("pixels.out"));
        solve();
//        pw.print(a);
        pw.close();
//            int b = solve2();
//            if (a != b) break;
//            pw.close();
//        }
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}