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 TaskC {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        Solve solve = new Solve();
        solve.solve(in, out);
        out.close();
    }

    private static class Solve {
        private final static long MOD = 1000000007L;
        private final static double EPS = 0.000001D;

        int[] used = new int[30];

        public void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            char[] s = in.next().toCharArray();
            for (char c : s) {
                used[c - 'a'] = 1;
            }
            if (k > n) {
                for (char c : s) {
                    out.print(c);
                }
                int small = 0;
                for (int i = 0; i < 26; i++) {
                    if (used[i] == 1) {
                        small = i;
                        break;
                    }
                }
                for (int i = n; i < k; i++) {
                    out.print((char)('a' + small));
                }
                return;
            }
            int max = -1;
            for (int i = 0; i < 26; i++) {
                if (used[i] == 1) max = i;
            }
            int len = k - 1;
            while (s[len] - 'a' == max) {
                len--;
            }
            for (int i = 0; i < len; i++) {
                out.print(s[i]);
            }
            int big = 0;
            for (int i = 25; i >= 0; i--) {
                if (used[i] == 1) {
                    if (i + 'a' > s[len]) {
                        big = i;
                    }
                }
            }
            int small = 0;
            for (int i = 0; i < 26; i++) {
                if (used[i] == 1) {
                    small = i;
                    break;
                }
            }
            out.print((char)('a' + big));
            for (int i = len + 1; i < k; i++) {
                out.print((char)('a' + small));
            }
        }


        private long pow(long n, long p) {
            if (p == 0) return 1;
            long x = pow(n, p / 2);
            x = (x * x) % MOD;
            if (p % 2 == 1) x = (x * n) % MOD;
            return x;
        }
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

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