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.StringTokenizer;
import java.util.TreeSet;

public class CFCC {

    public static void main(String[] args) throws IOException {
        MyScanner sc = new MyScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int N = sc.nextInt(), K = sc.nextInt();
        char[] c = sc.next().toCharArray();
        TreeSet<Character> set = new TreeSet<>();
        for (char ch : c) set.add(ch);
        if (K > N) {
            out.print(new String(c));
            for (int i = N; i < K; i++) out.print(set.first());
            out.println();
        } else {
            int chosen;
            for (chosen = K - 1; chosen >= 0; chosen--)
                if (set.higher(c[chosen]) != null) break;
            char[] res = new char[K];
            for (int i = 0; i < chosen; i++) res[i] = c[i];
            res[chosen] = set.higher(c[chosen]);
            for (int i = chosen + 1; i < K; i++) res[i] = set.first();
            out.println(new String(res));
        }
        out.flush();
        out.close();
    }

    private static class MyScanner {
        StringTokenizer st;
        BufferedReader br;

        public MyScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public MyScanner(String filename) throws IOException {
            br = new BufferedReader(new FileReader(new File(filename)));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}
