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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;

public class Task940C {

    public static class FastScanner {

        protected static final int STRBUFFERLENGTH = 0x1000;

        protected DataInputStream dataInputStream;
        protected byte[] buffer = new byte[0x10000];
        protected byte[] strbuffer = new byte[STRBUFFERLENGTH];
        protected int bufferOffset;
        protected int bufferLength;
        protected boolean isEndOfFile;

        public FastScanner() throws IOException {
            dataInputStream = new DataInputStream(System.in);
            Read();
        }

        public FastScanner(final String fileName) throws IOException {
            dataInputStream = new DataInputStream(new FileInputStream(fileName));
            Read();
        }

        protected void Read() throws IOException {
            final int length = dataInputStream.read(buffer);
            if (length > 0) {
                bufferLength = length;
            } else {
                bufferLength = 0;
                isEndOfFile = true;
            }
            bufferOffset = 0;
        }

        protected byte nextByte() throws IOException {
            if (bufferOffset == bufferLength) {
                if (!isEndOfFile) Read();
                if (isEndOfFile) return 0;
            }
            return buffer[bufferOffset++];
        }

        public int nextInt() throws IOException {
            int a = 0;
            boolean isNegative = false;

            byte b = nextByte();
            while (b <= ' ') b = nextByte();
            if (b == '-') {
                isNegative = true;
                b = nextByte();
            }
            while (b > ' ') {
                a = a * 10 + (b - '0');
                b = nextByte();
            }
            return isNegative ? -a : a;
        }

        public String nextLine() throws IOException {
            String s = "";
            int strbufferOffset = 0;

            byte b = nextByte();
            while (b <= ' ') b = nextByte();

            do {
                strbuffer[strbufferOffset++] = b;
                if (strbufferOffset >= STRBUFFERLENGTH) {
                    s += new String(strbuffer, 0, STRBUFFERLENGTH);
                    strbufferOffset = 0;
                }
                b = nextByte();
            } while (b != '\n' && b != '\r' && b != 0);
            s += new String(strbuffer, 0, strbufferOffset);

            return s;
        }

    }

    public static void main(final String[] args) throws IOException {
        final FastScanner scanner = new FastScanner();

        final int n = scanner.nextInt();
        final int k = scanner.nextInt();
        final String s = scanner.nextLine();

        final boolean[] used = new boolean[26];
        char minChar = s.charAt(0);
        for (int i = 0; i < n; i++) {
            final char c = s.charAt(i);
            used[c - 'a'] = true;
            if (c < minChar) minChar = c;
        }

        final StringBuilder stringBuilder;
        if (k > n) {
            stringBuilder = new StringBuilder(s);
            for (int i = 0; i < k - n; i++) {
                stringBuilder.append(minChar);
            }
        } else {
            stringBuilder = new StringBuilder(s.substring(0, k));
            int offset = k - 1;
            boolean incOk = false;
            do {
                int letterIndex = stringBuilder.charAt(offset) - 'a';
                for (int i = letterIndex + 1; i < 26; i++) {
                    if (used[i]) {
                        stringBuilder.setCharAt(offset, (char)('a' + i));
                        incOk = true;
                        break;
                    }
                }
                if (!incOk) {
                    stringBuilder.setCharAt(offset, minChar);
                    offset--;
                }
            }
            while (!incOk);

        }
        System.out.println(stringBuilder);
    }

}
