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 sun.reflect.generics.tree.Tree;

import java.io.*;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.*;


public class Newbie {

    static InputReader sc = new InputReader(System.in);
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) throws IOException {
        solver s = new solver();
        long t = 1;
        while (t > 0) {
            s.solve();
            t--;
        }
        out.close();
    }

   /* static class descend implements Comparator<pair1> {
        public int compare(pair1 o1, pair1 o2) {
            if (o1.pop != o2.pop)
                return (int) (o1.pop - o2.pop);
            else
                return o1.in - o2.in;
        }
    }*/

    static class InputReader {
        public BufferedReader br;
        public StringTokenizer token;

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

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

        public int ni() {
            return Integer.parseInt(sn());
        }

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

        public long nlo() {
            return Long.parseLong(sn());
        }

        public double nd() {
            return Double.parseDouble(sn());
        }

        public int[] na(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = sc.ni();
            return a;
        }

        public long[] nal(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = sc.nlo();
            return a;
        }
    }

    static class card {
        long a;
        int cnt;
        int i;

        public card(long a, int cnt, int i) {
            this.a = a;
            this.cnt = cnt;
            this.i = i;
        }
    }

    static class ascend implements Comparator<pair> {
        public int compare(pair o1, pair o2) {
            if (o1.a != o2.a)
                return (int) (o1.a - o2.a);
            else
                return (int) (o1.b - o2.b) * -1;
        }
    }

    static class extra {

        static boolean v[] = new boolean[100001];
        static List<Integer> l = new ArrayList<>();
        static int t;

        static void shuffle(int a[]) {
            for (int i = 0; i < a.length; i++) {
                int t = (int) Math.random() * a.length;
                int x = a[t];
                a[t] = a[i];
                a[i] = x;
            }
        }

        static void shufflel(long a[]) {
            for (int i = 0; i < a.length; i++) {
                int t = (int) Math.random() * a.length;
                long x = a[t];
                a[t] = a[i];
                a[i] = x;
            }
        }

        static long gcd(long a, long b) {
            if (b == 0)
                return a;
            else
                return gcd(b, a % b);
        }

        static boolean valid(int i, int j, int r, int c) {
            if (i >= 0 && i < r && j >= 0 && j < c) {
                // System.out.println(i+" /// "+j);
                return true;
            } else {
                //  System.out.println(i+" //f "+j);
                return false;
            }
        }

        static void seive() {
            for (int i = 2; i < 101; i++) {
                if (!v[i]) {
                    t++;
                    l.add(i);
                    for (int j = 2 * i; j < 101; j += i)
                        v[j] = true;
                }
            }
        }

        static int binary(LinkedList<Integer> a, long val, int n) {
            int mid = 0, l = 0, r = n - 1, ans = 0;
            while (l <= r) {
                mid = (l + r) >> 1;
                if (a.get(mid) == val) {
                    r = mid - 1;
                    ans = mid;
                } else if (a.get(mid) > val)
                    r = mid - 1;
                else {
                    l = mid + 1;
                    ans = l;
                }
            }
            return (ans + 1);
        }

        static long fastexpo(long x, long y) {
            long res = 1;
            while (y > 0) {
                if ((y & 1) == 1) {
                    res *= x;
                }
                y = y >> 1;
                x = x * x;
            }
            return res;
        }

        static long lfastexpo(long x, long y, long p) {
            long res = 1;
            x = x % p;
            while (y > 0) {
                if ((y & 1) == 1) {
                    res = (res * x) % p;
                }
                y = y >> 1;
                x = (x * x) % p;
            }
            return res;
        }

       /* void dijsktra(int s, List<pair> l[], int n) {
            PriorityQueue<pair> pq = new PriorityQueue<>(new ascend());
            int dist[] = new int[100005];
            boolean v[] = new boolean[100005];
            for (int i = 1; i <= n; i++)
                dist[i] = 1000000000;
            dist[s] = 0;
            for (int i = 1; i < n; i++) {
                if (i == s)
                    pq.add(new pair(s, 0));
                else
                    pq.add(new pair(i, 1000000000));
            }
            while (!pq.isEmpty()) {
                pair node = pq.remove();
                v[node.a] = true;
                for (int i = 0; i < l[node.a].size(); i++) {
                    int v1 = l[node.a].get(i).a;
                    int w = l[node.a].get(i).b;
                    if (v[v1])
                        continue;
                    if ((dist[node.a] + w) < dist[v1]) {
                        dist[v1] = dist[node.a] + w;
                        pq.add(new pair(v1, dist[v1]));
                    }
                }
            }
        }*/
    }

    static class pair {
        int a;
        int b;

        public pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
    }

    static class pair1 {
        pair p;
        int in;

        public pair1(pair a, int n) {
            this.p = a;
            this.in = n;
        }
    }

    static int inf = 5000013;

    static class solver {
        DecimalFormat df = new DecimalFormat("0.00");
        extra e = new extra();
        int mod = 1000000007;
        boolean v[] = new boolean[1000001];

        void solve() throws IOException {
            int n = sc.ni();
            int k = sc.ni();
            char c[] = sc.sn().toCharArray();
            TreeSet<Character> set = new TreeSet<>();
            char min = 'z';
            for (int i = 0; i < c.length; i++) {
                set.add(c[i]);
                if (c[i] < min)
                    min = c[i];
            }
            StringBuilder ans = new StringBuilder();
            if (k > n) {
                ans.append(String.valueOf(c));
                int d = k - n;
                while (d-- > 0)
                    ans.append(min);
            } else {
                char hi = ' ';
                ans.append(String.valueOf(Arrays.copyOfRange(c,0,k)));
                for (int i = ans.length() - 1; i >= 0; i--) {
                    try {
                        hi = set.higher(c[i]);
                        ans.setCharAt(i, hi);
                        break;
                    } catch (NullPointerException e) {
                        ans.setCharAt(i,min);
                        continue;
                    }
                }
            }
            System.out.println(ans);
        }
    }
}