Problem: Piegirl is buying stickers for a project. Stickers come on sheets, and each sheet of stickers contains exactly n stickers. Each sticker has exactly one character printed on it, so a sheet of stickers can be described by a string of length n. Piegirl wants to create a string s using stickers. She may buy as many sheets of stickers as she wants, and may specify any string of length n for the sheets, but all the sheets must be identical, so the string is the same for all sheets. Once she attains the sheets of stickers, she will take some of the stickers from the sheets and arrange (in any order) them to form s. Determine the minimum number of sheets she has to buy, and provide a string describing a possible sheet of stickers she should buy.

Input

The first line contains string s (1 ≤ |s| ≤ 1000), consisting of lowercase English characters only. The second line contains an integer n (1 ≤ n ≤ 1000).

Output

On the first line, print the minimum number of sheets Piegirl has to buy. On the second line, print a string consisting of n lower case English characters. This string should describe a sheet of stickers that Piegirl can buy in order to minimize the number of sheets. If Piegirl cannot possibly form the string s, print instead a single line with the number -1.

Examples

Input

banana
4


Output

2
baan


Input

banana
3


Output

3
nab


Input

banana
2


Output

-1

Note

In the second example, Piegirl can order 3 sheets of stickers with the characters "nab". She can take characters "nab" from the first sheet, "na" from the second, and "a" from the third, and arrange them to from "banana".

Solution (in JAVA):

Solution:



import java.io.*;
import java.text.DecimalFormat;
import java.util.*;
import java.awt.Point;

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();
        int t = 1;
        while (t > 0) {
            s.sol();
            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 ascend implements Comparator<pair> {
        public int compare(pair o1, pair o2) {
            return o2.b - o1.b;
        }
    }

    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 int gcd(int a, int 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("0.00000000");
        extra e = new extra();
        long mod = (long) (1000000007);

        void sol() throws IOException {
            String s = sc.sn();
            int n = s.length();
            int k = sc.ni();
            char c[] = s.toCharArray();
            int inf[] = new int[26];
            int add[] = new int[26];
            StringBuilder sb = new StringBuilder();
            int cnt = 0;
            for (int i = 0; i < n; i++) {
                if (inf[c[i] - 'a'] == 0) {
                    sb.append(c[i]);
                    cnt++;
                }
                inf[c[i] - 'a']++;
            }
            if (cnt > k) {
                System.out.println(-1);
                System.exit(0);
            }
            k -= cnt;
            PriorityQueue<Integer> pq = new PriorityQueue<>((x, y) -> ((int) Math.ceil((inf[x] * 1.0) / add[x]) - (int) Math.ceil((inf[y] * 1.0) / add[y])) * -1);
            for (int i = 0; i < 26; i++) {
                if (inf[i] > 0) {
                    add[i]++;
                    pq.add(i);
                }
            }
            while (k-- > 0 && !pq.isEmpty()) {
                int t = pq.poll();
                sb.append((char) (t + 'a'));
                add[t]++;
                pq.add(t);
            }
            int ans = -1;
            for (int i = 0; i < 26; i++) {
                if (inf[i] > 0)
                    ans = Math.max(ans, (int) Math.ceil((inf[i] * 1.0) / add[i]));
            }
            out.println(ans);
            out.println(sb);
        }
    }
}