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

public class Main {
    private static Scanner in = new Scanner(System.in);
    private static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int n = in.nextInt();
        int k = in.nextInt();
        String s = in.next();
        char[] chars = s.toCharArray();
        TreeSet<Character> t = new TreeSet<>();
        for (int i = 0; i < n; ++i) {
            t.add(chars[i]);
        }
        char[] res = new char[k];
        if (n < k) {
            int i = 0;
            for (; i < n; ++i) {
                out.print(chars[i]);
            }
            char first = t.first();
            for (;i < k; ++i) {
                out.print(first);
            }
        } else {
            for (int i = 0; i < k; ++i) {
                res[i] = chars[i];
            }
            char first = t.first();
            int index = k-1;
            while (index >= 0) {
                char curr = res[index];
                Character c = t.higher(curr);
                if (c != null) {
                    res[index] = c;
                    break;
                } else {
                    res[index] = first;
                    index--;
                }
            }
            for (int i = 0; i < k; ++i)
                out.print(res[i]);
        }
        out.close();
    }
}
