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 codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    long MOD = 1000000007L;
    int INF = 1000000001;
    
    public class Obj implements Comparable<Obj>{
        public int start;
        public int end;
        
        public Obj(int start_, int end_){
            this.start = start_;
            this.end = end_;

        }
        
        public int compareTo(Obj other){
            if (other.start == this.start){
                return this.end - other.end;
            }
            return this.start - other.start;
        }

    }
    
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
        Codechef cf = new Codechef();
        cf.Solve();
	}
	
	int[][] dp;
	public void Solve(){
        MyScanner sc = new MyScanner();
        int n = sc.nextInt();
        int k = sc.nextInt();
        String s = sc.nextLine();
        char[] arr = s.toCharArray();
        char[] res = new char[k];
        int[] cnt = new int[26];
        for (int i = 0; i < n; ++i){
            int idx = (int)(arr[i] - 'a');
            cnt[idx]++;
        }
        out = new PrintWriter(new BufferedOutputStream(System.out));
        if (k > n){
            for (int i = 0; i < n; ++i){
                res[i] = arr[i];
            }
            for (int i = n; i < k; ++i){
                res[i] = findFirst(cnt);
            }
        }else{
            int ptn = k - 1;
            boolean ok = false;
            char first = findFirst(cnt);
            for(;ptn >= 0; --ptn){
                int idx = (int)(arr[ptn] - 'a');
                char c = findLast(cnt, idx);
                if (c != arr[ptn]){
                    res[ptn] = c;
                    ok = true;
                    break;
                }else{
                    res[ptn] = first;
                }
            }
            
            for (int i = 0; i < ptn; ++i){
                res[i] = arr[i];
            }
        }
        
        for (int i = 0; i < k; ++i){
            out.print(res[i]);
        }
        
        out.close();
	}
	
	public char findFirst(int[] cnt){
	    for (int i = 0; i < 26; ++i){
	        if (cnt[i] != 0){
	            return (char)(i + 'a');
	        }
	    }
	    return 0;
	}
	
	public char findLast(int[] cnt, int idx){
	    int res = -1;
	    for (int i = 25; i > idx; --i){
	        if (cnt[i] != 0){
	            res = i;
	        }
	    }
	    if (res == -1)
	        return (char)(idx + 'a');
	    else{
	        return (char)(res + 'a');
	    }
	}
	
	
	//-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
      try {
         str = br.readLine();
      } catch (IOException e) {
         e.printStackTrace();
      }
      return str;
      }

   }
}
