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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UnsupportedEncodingException;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws UnsupportedEncodingException, IOException {
        Reader.init(System.in);
        StringBuilder out = new StringBuilder();
        int n = Reader.nextInt(), k = Reader.nextInt();
        char[] str = Reader.nextLine().toCharArray();
        boolean[] v = new boolean[26];
        for(int i = 0; i < n; i++)
            v[str[i] - 'a'] = true;
        char[] t = new char[k];
        int min = Math.min(n, k);
        for(int i = 0; i < min; i++)
            t[i] = str[i];
        if(k > n) {
            for(int i = 0; i < 26; i++)
                if(v[i]) {
                    for(int j = min; j < k; j++)
                        t[j] = (char) (i + 'a');
                    break;
                }
        } else {
            out :
            for(int i = min - 1, j; i > -1; i--)
                for(j = t[i] - 'a' + 1; j < 26; j++)
                    if(v[j]) {
                        t[i] = (char) (j + 'a');
                        for(int l = 0; l < 26; l++)
                            if(v[l]) {
                                for(int m = i + 1; m < min; m++)
                                    t[m] = (char) (l + 'a');
                                break out;
                            }
                        break out;
                    }
        }
        for(char c : t)
            out.append(c);
        out.append('\n');
        PrintWriter pw = new PrintWriter(System.out);
        pw.print(out);
        pw.close();
    }
    
}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    static void init(InputStream input) throws UnsupportedEncodingException {
        reader = new BufferedReader(
                new InputStreamReader(input, "UTF-8"));
        tokenizer = new StringTokenizer("");
    }
    
    static void init(String url) throws FileNotFoundException {
        reader = new BufferedReader(new FileReader(url));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

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

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}