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.InputStreamReader;
import java.util.Arrays;
import java.util.NavigableSet;
import java.util.TreeSet;

public class PhoneNumbers {

    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String[] firstLine = reader.readLine().split(" ");
        int sourceLength = Integer.parseInt(firstLine[0]);
        int resultLength = Integer.parseInt(firstLine[1]);
        char[] source = reader.readLine().toCharArray();
        NavigableSet<Character> alphabet = new TreeSet<>();
        for (char c : source) {
            alphabet.add(c);
        }
        char firstChar = alphabet.first();
        char lastChar = alphabet.last();

        char[] result = new char[resultLength];
        System.arraycopy(source, 0, result, 0, Math.min(resultLength, sourceLength));
        if (resultLength > sourceLength) {
            Arrays.fill(result, sourceLength, resultLength, firstChar);
            System.out.println(result);
            return;
        }
        for (int i = result.length - 1; i >= 0; i--) {
            if (result[i] < lastChar) {
                result[i] = alphabet.higher(result[i]);
                System.out.println(result);
                return;
            }
            result[i] = firstChar;
        }
    }
}
