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.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.StringTokenizer;

public class CF_466A {

	public static void main(String[] args) throws IOException {
		reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = null;
        
        int n = nextInt();
        int k = nextInt();
        String s = nextToken();
        
        char[] c = s.toCharArray();
        Arrays.sort(c);
        ArrayList<Character> ch = new ArrayList<Character>();
        HashMap<Character,Integer> hash = new HashMap<>();
        for(int i = 0 ; i < c.length;i++)
        	if(!hash.containsKey(c[i]))
        	{
        		hash.put(c[i], ch.size());
        		ch.add(c[i]);
        	}
        String result = "";
        if(n < k)
        {
        	char[] res = new char[k];
        	for(int i = 0 ; i < k;i++)
        		if(i < n)
        			res[i] = s.charAt(i);
        		else
        			res[i] = c[0];
        	result = new String(res);
        }else
        {
        	char[] res = new char[k];
        	boolean less = false;
        	for(int i = k-1;i >= 0 ;i--)
        	{
        		int sIndex = hash.get(s.charAt(i));
        		if(sIndex != ch.size()-1)
        			sIndex++;
        		else
        			sIndex = 0;
        		
        		if(less)
        			res[i] = s.charAt(i);
        		else
        		{
        			less = sIndex != 0;
        			res[i] = ch.get(sIndex);
        		}
        	}
        	result = new String(res);
        }
        System.out.println(result);
	}
	

    static BufferedReader reader;
    static StringTokenizer tokenizer;

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

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

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

    static String nextToken() throws IOException
    {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
        {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

}
