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.
//package codeforces;

import java.util.Scanner;

public class phone {

	public static void main(String[] args) { 
		Scanner input=new Scanner(System.in);
		int s1 = input.nextInt();
		int sRet = input.nextInt();
		String s = input.next();
		
		char min = 'z';
		char max = 'a';
		for(int i = 0; i<s1; i++) {
			if(s.charAt(i)<min)
				min = s.charAt(i);
			else if(s.charAt(i)>max)
				max = s.charAt(i);
		}
		
		if(sRet>s1) {
			System.out.print(s);
			for(int j = 0; j<sRet-s1; j++) {
				System.out.print(min);
			}
		}
		
		else {
			int[] ch = new int[s1];
			int[] chs = new int[26];
		
			for(int i = 0; i<s1; i++) {
				ch[i] = s.charAt(i)-97;
				chs[s.charAt(i)-97]++;
			}
			
			int ind = sRet-1;
			for(int j = sRet-1; j>=0; j--) {
				if(ch[j]+97 != (int)max) {
					ind = j;
					break;
				}
			}
			
			System.out.print(s.substring(0,ind));
			
			for(int k = ch[ind]+1; k<26; k++) {
				if(chs[k]>0) {
					System.out.print((char)(k+97));
					break;
				}
			}
			
			for(int l = 0; l<sRet-ind-1; l++) {
				System.out.print(min);
			}
		}
		
		input.close(); 
     } 
}
