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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ProblemCPhoneNumbers solver = new ProblemCPhoneNumbers();
        solver.solve(1, in, out);
        out.close();
    }

    static class ProblemCPhoneNumbers {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int sl = in.nextInt();
            int k = in.nextInt();
            StringBuilder s = new StringBuilder(in.next());
            StringBuilder ans = new StringBuilder("");
            if (k <= sl) {
                int a[] = new int[26];
                for (int i = 0; i < sl; i++) {
                    a[s.charAt(i) - 'a'] = 1;
                }
                int ng[] = new int[26];
                for (int i = 0; i < 26; i++) {
                    for (int j = i + 1; j < 26; j++) {
                        if (a[j] == 1) {
                            ng[i] = j;
                            break;
                        }
                    }
                }
                for (int i = k - 1; i >= 0; i--) {
                    if (ng[s.charAt(i) - 'a'] != 0) {
                        char ic = (char) (ng[s.charAt(i) - 'a'] + 'a');
                        ans.append(s.substring(0, i) + ic);
                        int j = 0;
                        for (j = 0; j < 26; j++) {
                            if (a[j] != 0) {
                                break;
                            }
                        }
                        ic = (char) (j + 'a');
                        for (j = i + 1; j < k; j++) {
                            ans.append(ic);
                        }
                        break;
                    }
                }
            } else {
                ans.append(s.toString());
                int a[] = new int[26];
                for (int i = 0; i < sl; i++) {
                    a[s.charAt(i) - 'a'] = 1;
                }
                int j = 0;
                for (j = 0; j < 26; j++) {
                    if (a[j] != 0) {
                        break;
                    }
                }
                char ic = (char) (j + 'a');
                for (int i = sl; i < k; i++) {
                    ans.append(ic);
                }
            }
            out.println(ans);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(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 (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}

