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.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(), k = in.nextInt();
            String s = in.next();
            char[] a = s.toCharArray();
            boolean[] got = new boolean[26];
            char max = 'a';
            char min = 'z';
            for (char x : a) {
                got[x - 'a'] = true;
                if (x < min) min = x;
                if (x > max) max = x;
            }
            if (k == n) {
                for (int i = n - 1; i >= 0; --i) {
                    if (a[i] == max) continue;
                    for (int j = (a[i] - 'a') + 1; j < 26; ++j) {
                        if (got[j]) {
                            max = (char) (j + 'a');
                            break;
                        }
                    }
                    StringBuilder res = new StringBuilder(s.substring(0, i) + max);
                    while (res.length() < n) res.append(min);
                    out.println(res.toString());
                    return;
                }
            } else if (k > n) {
                StringBuilder res = new StringBuilder(s);
                while (res.length() < k) res.append(min);
                out.println(res.toString());
            } else {
                StringBuilder res = new StringBuilder(s.substring(0, k));
                for (int i = k - 1; i >= 0; --i) {
                    max = res.charAt(i);
                    for (int j = (max - 'a') + 1; j < 26; ++j) {
                        if (got[j]) {
                            StringBuilder r = new StringBuilder(res.toString().substring(0, i) + (char) (j + 'a'));
                            while (r.length() < k) r.append(min);
                            out.println(r.toString());
                            return;
                        }
                    }
                }
            }
        }

    }

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

    }
}

