Problem:
Score : 400 points

Problem Statement

Find the largest integer that can be formed with exactly N matchsticks, under the following conditions:

Every digit in the integer must be one of the digits A_1, A_2, ..., A_M (1 \leq A_i \leq 9).

The number of matchsticks used to form digits 1, 2, 3, 4, 5, 6, 7, 8, 9 should be 2, 5, 5, 4, 5, 6, 3, 7, 6, respectively.

Constraints

All values in input are integers.

2 \leq N \leq 10^4

1 \leq M \leq 9

1 \leq A_i \leq 9

A_i are all different.

There exists an integer that can be formed by exactly N matchsticks under the conditions.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 ... A_M

Output

Print the largest integer that can be formed with exactly N matchsticks under the conditions in the problem statement.

Sample Input 1

20 4
3 7 8 4

Sample Output 1

777773

The integer 777773 can be formed with 3 + 3 + 3 + 3 + 3 + 5 = 20 matchsticks, and this is the largest integer that can be formed by 20 matchsticks under the conditions.

Sample Input 2

101 9
9 8 7 6 5 4 3 2 1

Sample Output 2

71111111111111111111111111111111111111111111111111

The output may not fit into a 64-bit integer type.

Sample Input 3

15 3
5 4 6

Sample Output 3

654

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
    static class Solver {
        int m ;
        int[] arr = {0,2,5,5,4,5,6,3,7,6};
        int[] matches;
        String[] dp;
        public void solve(MyReader in, PrintWriter out) {
            int n = in.nextInt();
            m = in.nextInt();

            matches = new int[m];

            dp = new String[10005];

            for (int i = 0; i < m; i++) {
                matches[i] = in.nextInt();
            }

            out.println(calc(n));
        }

        String calc(int n){
            if(n < 0)return null;
            if (n==0)return "";
            if (dp[n] != null)return dp[n];

            String res = null;
            for (int i= 0;i<m;i++){
                StringBuilder tmp = new StringBuilder(matches[i]+"");
                String finRes = calc(n - arr[matches[i]]);
                if (finRes == null)continue;
                tmp.append(finRes);
                String tmpRes = tmp.toString();

                if (res==null || tmpRes.length() > res.length())
                    res = tmpRes;
                else if(tmpRes.length() == res.length() && tmpRes.compareTo(res) > 0)
                    res = tmpRes;

            }

            return dp[n] = res;
        }


    }

    public static void main(String[] args) {
        MyReader mr = new MyReader();
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        new Solver().solve(mr, out);
        out.close();
    }

    //////////////////////////////////////////////////////////////////////////
    //    static int[][] dir = {{0,1}, {1,0},{-1,0}, {0,-1}};
//    static int[][] dir = {{0,1}, {1,0},{-1,0}, {0,-1}, {-1,-1},{-1,1}, {1,1}, {1,-1}};
    static class MyReader {
        BufferedReader br;
        StringTokenizer st;

        MyReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }

            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String res = "";
            try {
                res = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return res;
        }

        int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }

            return arr;
        }

        Integer[] nextIntegerArray(int n) {
            Integer[] arr = new Integer[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }

            return arr;
        }

        Long[] nextLongArray(int n) {
            Long[] arr = new Long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }

            return arr;
        }

        long[] nextlongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }

            return arr;
        }

        String[] nextStringArray(int n) {
            String[] arr = new String[n];
            for (int i = 0; i < n; i++) {
                arr[i] = next();
            }
            return arr;
        }
    }

    /////////////////////////////////////////////////////////////    

    static class Pair<K, V> {
        K x;
        V y;

        public Pair(K x, V y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair<?, ?> pair = (Pair<?, ?>) o;
            return Objects.equals(x, pair.x) &&
                    Objects.equals(y, pair.y);
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }
    }


    /////////////////////////////////////////////////////////////

    static <T> void swap(T[] arr, int i, int j) {
        T tmp = arr[i];
        arr[i] = arr[j];
        arr[j] = tmp;
    }

}