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.Scanner;
import java.util.Set;
import java.util.TreeSet;
import java.util.ArrayList;

/**
 * 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;
        Scanner in = new Scanner(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, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            String s = in.next();

            Set<Character> c = new TreeSet<>();
            for (int i = 0; i < n; i++) c.add(s.charAt(i));

            ArrayList<Character> cList = new ArrayList<>(c);

            StringBuilder sb = new StringBuilder();
            if (k > n) {
                sb.append(s);
                while (sb.length() < k) {
                    sb.append(cList.get(0));
                }
                out.println(sb);
                return;
            }

            for (int i = k - 1; i >= 0; i--) {
                if (i < n) {
                    char cc = s.charAt(i);
                    int index = cList.indexOf(cc);
                    if (index == cList.size() - 1) {
                        sb.append(cList.get(0));
                    } else {
                        sb.append(cList.get(index + 1));
                        break;
                    }
                } else {
                    sb.append(cList.get(0));
                }
            }
            sb.reverse();
            if (sb.length() < k) {
                sb.insert(0, s.substring(0, k - sb.length()));
            }
            out.println(sb);
        }

    }
}

