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.
// Don't place your source in a package
import java.lang.reflect.Array;
import java.text.DecimalFormat;
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
import java.util.stream.Stream;


// Please name your class Main
public class Main {
    static FastScanner fs=new FastScanner();
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next() {
            while (!st.hasMoreElements())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        int Int() {
            return Integer.parseInt(next());
        }

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

        String Str(){
            return next();
        }
    }


    public static void main (String[] args) throws java.lang.Exception {
        PrintWriter out = new PrintWriter(System.out);

        int T=1;
        for(int t=0;t<T;t++){
            int n=Int(),k=Int();
            String s=Str();

            Solution sol=new Solution(out);
            sol.solution(s,k);
        }
        out.flush();

    }


    public static int Int(){
        return fs.Int();
    }
    public static long Long(){
        return fs.Long();
    }
    public static String Str(){
        return fs.Str();
    }

}






class Solution{
    PrintWriter out;
    public Solution(PrintWriter out){
        this.out=out;
    }


    public void solution(String s,int k){
        StringBuilder str=new StringBuilder();
        Set<Character>set=new HashSet<>();
        for(char c:s.toCharArray()){
            set.add(c);
        }

        List<Character>list=new ArrayList<>(set);
        Collections.sort(list);

        if(k>s.length()){
            str.append(s);
            for(int i=s.length();i<k;i++){
                str.append(list.get(0)+"");
            }
        }
        else{
            for(int i=k-1;i>=0;i--){
                char c=s.charAt(i);
                int pos=-1;
                for(int j=0;j<list.size();j++){
                    if(list.get(j)>c){
                        pos=j;
                        break;
                    }
                }
                if(pos!=-1){
                    str.append(s.substring(0,i));
                    str.append(list.get(pos)+"");
                    for(int j=str.length();j<k;j++){
                        str.append(list.get(0));
                    }
                    break;
                }
            }
        }
        out.println(str.toString());
    }


}



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                      free bug dog
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