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

public class C {

    public static void main(String[] args) {
        MyScanner scan = new MyScanner();
        int n = scan.nextInt();
        int k = scan.nextInt();
        String s = scan.nextLine();

        int[] arr = new int[26];
        for (char ch: s.toCharArray()) {
            int i = ch - 'a';
            arr[i] = 1;
        }

        int min_char = -1;
        for (int i = 0; i < 25; ++ i) {
            if (arr[i] == 0) continue;
            if (min_char == -1) min_char = i;
            for (int j = i + 1; j < 26; ++ j) {
                if (arr[j] > 0) {
                    arr[i] = j;
                    break;
                }
            }
        }
        for (int i = 25; i >= 0; -- i) {
            if (arr[i] > 0) {
                arr[i] = -1;
                if (min_char == -1) min_char = i;
                break;
            }
        }

        if (k > n) {
            StringBuilder sb = new StringBuilder(s);
            for (int i = 0; i < k - n; ++ i) {
                sb.append((char)(min_char + 'a'));
            }
            System.out.println(sb.toString());
            return;
        }

        /*for (int i = 0; i < 26; ++ i) {
            System.out.print(arr[i] + "  ");
        }
        System.out.println("");*/

        char[] tt = s.toCharArray();
        int idx = -1;
        for (int i = k - 1; i >= 0; -- i) {
            if (arr[tt[i]-'a'] == -1) continue;
            idx = i;
            break;
        }
        //System.out.println(idx);

        tt[idx] = (char)((char)arr[tt[idx]-'a'] + 'a');
        for (int i = idx + 1; i < k; ++ i) {
            tt[i] = (char) (min_char + 'a');
        }
        for (int i = 0; i < k; ++ i) {
            System.out.print(tt[i]);
        }
        System.out.println("");
    }

    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;
        }
    }
}
