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.ByteArrayInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.List;
import java.util.NavigableSet;
import java.util.Queue;
import java.util.Set;
import java.util.TreeSet;
import java.util.logging.Level;
import java.util.logging.Logger;

/*
 *
 * @author ssaxena36 :D
 *
 */
public class NewClass {

    class Node {

        int data;
        Node left, right;

        Node(int data) {
            this.data = data;
            left = right = null;
        }
    }

    void solve() {
        int n = inpi();
        int k = inpi();
        String string = inps();
        NavigableSet<Character> set = new TreeSet<>();
        for (int i = 0; i < n; i++) {
            set.add(string.charAt(i));
        }
       // System.out.println(set);
        StringBuilder sb = null;
        if (k > n) {
            sb = new StringBuilder(string);
            char smallest = set.first();
            for (int i = n + 1; i <= k; i++) {
                sb.append(smallest);
            }
        } else {
            sb = new StringBuilder(string.substring(0, k));
            char c = set.first();
            for (int i = k - 1; i >= 0; i--) {
                Character higher = set.higher(sb.charAt(i));
                if (higher == null) {
                    sb.setCharAt(i, c);
                } else {
                    sb.setCharAt(i, higher);
                    break;
                }
            }
        }
        out.println(sb);

    }

    public boolean isPrime(long n) {
        return BigInteger.valueOf(n).isProbablePrime(5);
    }

    public boolean[] SieveOfEratosthenes(int n) {
        boolean prime[] = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p] == true) {
                for (int i = p * 2; i <= n; i += p) {
                    prime[i] = false;
                }
            }
        }
        for (int i = 2; i < n; i++) {
            if (prime[i]) {
                //do some stuff
            }
        }
        return prime;
    }
    InputStream obj;
    PrintWriter out;
    String check = "";
    int len;

    public static void main(String[] args) throws IOException {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    new NewClass().main1();
                } catch (IOException ex) {
                    Logger.getLogger(NewClass.class.getName()).log(Level.SEVERE, null, ex);
                }
            }
        }, "child-thread", 1 << 26).start();

    }

    void main1() throws IOException {
        out = new PrintWriter(System.out);
        obj = check.isEmpty() ? System.in : new ByteArrayInputStream(check.getBytes());
        //   obj=check.isEmpty() ? new FileInputStream("/home/ssaxena36/Desktop/file.in") : new ByteArrayInputStream(check.getBytes());
        solve();
        out.flush();
        out.close();
    }
    byte inbuffer[] = new byte[1024];
    int lenbuffer = 0, ptrbuffer = 0;

    int readByte() {
        if (lenbuffer == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuffer >= lenbuffer) {
            ptrbuffer = 0;
            try {
                lenbuffer = obj.read(inbuffer);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        if (lenbuffer <= 0) {
            return -1;
        }
        return inbuffer[ptrbuffer++];
    }

    boolean isSpaceChar(int c) {
        return (!(c >= 33 && c <= 126));
    }

    @SuppressWarnings("empty-statement")
    int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }

    String inps() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    @SuppressWarnings("empty-statement")
    int inpi() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    long inpl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    float inpf() {
        return Float.parseFloat(inps());
    }

    double inpd() {
        return Double.parseDouble(inps());
    }

    char inpc() {
        return (char) skip();
    }

    int[] inpia(int n) {
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = inpi();
        }
        return a;
    }

    long[] inpla(int n) {
        long a[] = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = inpl();
        }
        return a;
    }

    String[] inpsa(int n) {
        String a[] = new String[n];
        for (int i = 0; i < n; i++) {
            a[i] = inps();
        }
        return a;
    }

    double[][] inpdm(int n, int m) {
        double a[][] = new double[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                a[i][j] = inpd();
            }
        }
        return a;
    }

    int[][] inpim(int n, int m) {
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                a[i][j] = inpi();
            }
        }
        return a;
    }
}
