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.*;
 
/* Name of the class has to be "Main" only if the class is public. */
public class final2
{
	
    public static void main (String[] args) 
    {
        Scanner sc = new Scanner(System.in);

        int t=1;
        PrintWriter out=new PrintWriter(System.out);
        Set<Character> st=new HashSet<Character>();
        Set<String> st1=new HashSet<String>();
        int i,j,x=0,y=0,n=2,m,k;
        int d;
        int c=0,count=0;
        int sum1,sum=0;
        int min1,min;
        int pos=1;  
        String s,s1="";
        
        int max=Integer.MIN_VALUE;
        for(;t>0;t--)
        {
        	n=sc.nextInt();
        	k=sc.nextInt();
        	s=sc.next();
        	int arr[]=new int[26];
        	boolean brr[]=new boolean[26];
        	for(i=0;i<n;i++)
        		brr[s.charAt(i)-97]=true;
        	min=-1;
        	for(i=25;i>=0;i--)
        	{
        		arr[i]=min;
        		if(brr[i]==true)
        			min=i+97;
        		if(brr[i]==true)
        			c++;
        	}
        	if(c==1 &&k<=n)
        		out.println("No");
        	else
        	{
        		s1="";
        		boolean f=false,f1=false;
        		for(i=k-1;i>=0;i--)
        		{
        			if(k>n)
        			{
        				f1=true;
        				if(i>=n)
        				s1=(char)min+s1;
        				else
        					s1=s.charAt(i)+s1;
        			}
        			else if(f1)
        				s1=s.charAt(i)+s1;
        			else
        			{
        				if(arr[s.charAt(i)-97]>0)
        				{
        					s1=(char)arr[s.charAt(i)-97]+s1;
        					f1=true;
        				}
        				else
        				{
        					s1=(char)(min)+s1;
        				}
        			}
        		}
        		if(f1)
        			out.println(s1);
        		else
        			out.println("No");
        	}
        	//String s2=s.substring(0,k);
        }
        out.close();
        
    
        
        
    }
}