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.*;
import java.io.*;
public class C940
{
	public static void main(String args[]) throws Exception
	{
		BufferedReader f=new BufferedReader(new InputStreamReader(System.in));
		// BufferedReader f=new BufferedReader(new FileReader("C940.in"));
		StringTokenizer st=new StringTokenizer(f.readLine());
		int size1=Integer.parseInt(st.nextToken());
		int size2=Integer.parseInt(st.nextToken());
		String input=f.readLine();
		TreeSet<String> usable=new TreeSet<String>();
		for(int x=0;x<input.length();x++)
			usable.add(input.substring(x,x+1));
		if(size1<size2)
		{
			String[] arr=new String[size2];
			for(int x=0;x<size1;x++)
				arr[x]=input.substring(x,x+1);
			for(int x=size1;x<size2;x++)
				arr[x]=usable.first();
			for(int x=0;x<size2;x++)
				System.out.print(arr[x]);
			System.out.println();
		}
		else
		{
			String[] arr=new String[size2];
			for(int x=0;x<size2;x++)
				arr[x]=input.substring(x,x+1);
			arr[arr.length-1]=usable.higher(arr[arr.length-1]);
			int pos=arr.length-1;
			while(pos>=1&&arr[pos]==null)
			{
				arr[pos]=usable.first();
				arr[pos-1]=usable.higher(arr[pos-1]);
				pos--;
			}
			for(int x=0;x<size2;x++)
				System.out.print(arr[x]);
			System.out.println();
		}
	}
}