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 PhoneNumbers {


  public static void main(String[] args) {
    InputStream stream = System.in;
    PrintWriter out = new PrintWriter(System.out);
    FastReader sc = new FastReader(stream);
    //int t = sc.nextInt();
    Solver solver = new Solver();
    int t = 1;
    while(t-->0) {
      solver.solve(sc,out);
    }
    out.close();
  }
  
  static class Solver {
    public void solve(FastReader sc, PrintWriter out) {
      int n = sc.nextInt();
      int k = sc.nextInt();
      char[] s = sc.next().toCharArray();
      int[] cnt = new int[26];
      for(char c : s) cnt[c-'a']++;
      if(k>n) {
        char min = 'z';
        for(int i = 0; i < 26; i++) {
          if(cnt[i]>0) {
            min = (char)(i+'a');
            break;
          }
        }
        StringBuilder ans = new StringBuilder(new String(s));
        for(int i = n; i < k; i++) ans.append(min);
        out.println(ans);
        return;
      }
      StringBuilder ans = new StringBuilder();
      char min = 'z';
      for(int i = 0; i < 26; i++) {
        if(cnt[i]>0) {
          min = (char)(i+'a');
          break;
        }
      }
      for(int i = k-1; i >= 0; i--) {
        int now = s[i]-'a';
        boolean haveBig = false;
        for(int j = now+1; j < 26; j++) {
          if(cnt[j]==0) continue;
          haveBig = true;
          now = j;
          break;
        }
        if(haveBig) {
          ans.append((char)(now+'a'));
          while(--i>=0) {
            ans.append(s[i]);
          }
          break;
        } else {
          ans.append(min);
        }
      }
      out.println(ans.reverse());
    }
  }
  
  static class FastReader {
    InputStream stream;
    byte[] buf = new byte[1024];
    int curChar, numChars;
    public FastReader(InputStream stream) {
      this.stream = stream;
    }
    
    public int read() {
      if(numChars==-1) {
        throw new InputMismatchException();
      }
      if(curChar>=numChars) {
        curChar = 0;
        try {
          numChars = stream.read(buf);
        } catch(IOException e) {
          throw new InputMismatchException();
        }
        if(numChars<=0) {
          return -1;
        }
      }
      return buf[curChar++];
    }
    
    public int nextInt() {
      int c = read();
      while(isWhiteSpace(c)) c = read();
      int sign = 1;
      if(c == '-') {
        sign = -1;
        c = read();
      }
      int res = 0;
      do {
        if(c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c-'0';
        c = read();
      } while(!isWhiteSpace(c));
      return res*sign;
    }
    
    public long nextLong() {
      int c = read();
      while(isWhiteSpace(c)) c = read();
      int sign = 1;
      if(c == '-') {
        sign = -1;
        c = read();
      }
      long res = 0;
      do {
        if(c < '0' || c > '9') {
          throw new InputMismatchException();
        }
        res *= 10;
        res += c-'0';
        c = read();
      } while(!isWhiteSpace(c));
      return res*sign;
    }
    
    public String next() {
      int c = read();
      while(isWhiteSpace(c)) c = read();
      StringBuilder res = new StringBuilder();
      do {
        if(Character.isValidCodePoint(c)) {
          res.appendCodePoint(c);
        }
        c = read();;
      } while(!isWhiteSpace(c));
      return res.toString();
    }
    
    public boolean isWhiteSpace(int c) {
      return c == ' ' || c == '\n' ||
             c == '\r' || c == '\t' ||
             c == -1;
    }
  }
}
