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 cf_29 {
    public static void main(String[] args) {
        new Solution().solve();
    }
}

class Solution {
    public void solve() {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt(), k = fs.nextInt();
        String s = fs.next();
        char[] cArr = s.toCharArray();
        char[] result = new char[k];
        char max = cArr[0];
        char min = cArr[0];
        for (char c : cArr) {
            max = (char)Math.max(c, max);
            min = (char)Math.min(c, min);
        }
        if (n < k) {
            for (int i=0; i<n; i++) {
                result[i] = cArr[i];
            }
            for (int i=n; i <k; i++) {
                result[i] = min;
            }
        } else { // n >= k
            int len = n;
            for (int i=k-1; i >=0; i--) {
                if (cArr[i] != max) {
                    len = i;
                    break;
                }
            }
            char minOverLen = max;
            for (int i=0; i < n; i++) {
                if (cArr[i] > cArr[len]) {
                    minOverLen = (char)Math.min(cArr[i], minOverLen);
                }
            }
            for (int i=0; i < len; i++) {
                result[i] = cArr[i];
            }
            result[len] = minOverLen;
            for (int i=len+1; i <k; i++) {
                result[i] = min;
            }
        }
        System.out.println(new String(result));
    }
}

class FastScanner {
    private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private StringTokenizer st = new StringTokenizer("");
    
    // Below would return next string (delimited by space or new line)
    public String next() {
        while (!st.hasMoreTokens())
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        return st.nextToken();
    }

    // Below would return entire string in the line (including spaces)
    public String nextLineStr() {
        String str = "";
        try {
            str = br.readLine();
        } catch (IOException e) {
            e.printStackTrace();
        }
        return str;
    }
    
    public int[] readIntArray(int n) {
        int[] arr = new int[n];
        for (int i=0; i<n; i++) {
            arr[i] = nextInt();
        }
        return arr;
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }    
    
    public long nextLong() {
        return Long.parseLong(next());
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public float nextFloat() {
        return Float.parseFloat(next());
    }    
}