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.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		
		Scanner scaner = new Scanner(System.in);
		try {
        int n = scaner.nextInt();
        int k = scaner.nextInt();
        String a = scaner.next();
        
        List<Character> symbols = new ArrayList<>();
        char[] stringMas = a.toCharArray();
        for(int i = 0; i < n ; ++i)
        		if(!symbols.contains(stringMas[i]))
        			symbols.add(stringMas[i]);
        Collections.sort(symbols);
        
        String res;
        
        if(k>n){
        		res = a.concat(getStringForChar(symbols.get(0).toString().charAt(0), k-n));
        }
        else {
        		res = a.substring(0, k);
        		res = getLittleString(symbols,res);
        }
		
		System.out.print(res);
		}finally{
			scaner.close();
		}
	}
	
	private static String getStringForChar(char c, int lenght){
		char[] res = new char[lenght];
		for(int i = 0; i < lenght; ++i)
			res[i] = c;
		
		return new String(res);
	}
	
	private static String getLittleString(List<Character> symbols, String string ){
		char[] res = string.toCharArray();
		for(int i = string.length() - 1; i >=0; --i)
			if(string.charAt(i) == symbols.get(symbols.size() - 1))
				res[i] = symbols.get(0);
			else {
				res[i] = symbols.get(symbols.indexOf(string.charAt(i)) + 1);
				break;
			}
		return new String(res);
	}
}
