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.IOException;
import java.io.InputStreamReader;
import java.util.*;

import static java.lang.Math.*;

public class Main2 {

    private FastScanner scanner = new FastScanner();

    public static void main(String[] args) {
        new Main2().solve();
    }

    private void solve() {

        int n = scanner.nextInt(), k = scanner.nextInt();
        char[] c = scanner.nextLine().toCharArray();


        int a[] = new int[27], min = Integer.MAX_VALUE;
        for (int i = 0; i < n; i++) {
            a[c[i]- 'a'] = 1;
            min = Math.min(min, c[i] - 'a');
        }


        if (n < k) {
            char [] ans = new char[k];
            Arrays.fill(ans, (char) (min + 'a'));
            System.arraycopy(c, 0, ans, 0, n);
            System.out.println(String.valueOf(ans));
        } else {

            char [] ans = new char[k];
            System.arraycopy(c, 0, ans, 0, k);


            for (int i = k - 1; i >= 0; i--) {
                int cur = c[i] - 'a';
                char ch = '-';

                for (int j = cur + 1; j < 27; j++) {
                    if (a[j] != 0 && j != cur) {
                        ch = (char) ('a' + j);
                        break;
                    }
                }

                if (ch != '-') {
                    ans[i] = ch;
                    break;
                } else {
                    ans[i] = (char) (min + 'a');
                }
            }
            System.out.println(String.valueOf(ans));
        }

    }

    class Pair {
        int c, f;
    }

    class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;

        FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();

        }

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

        Integer[] nextA(int n) {
            Integer a[] = new Integer[n];
            for (int i = 0; i < n; i++) {
                a[i] = scanner.nextInt();
            }
            return a;
        }

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}