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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;

namespace ConsoleApp2
{
    class Program
    {
        static readonly int[] Matches = { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };

        static void ReadInt2(out int first, out int second)
        {
            var array = Console.ReadLine().Split().Select(s => int.Parse(s)).ToArray();
            first = array[0];
            second = array[1];
        }

        static string Max(string left, string right)
        {
            if (left == null || left.Contains("/"))
                return right;
            if (right == null || right.Contains("/"))
                return left;

            if (left.Length > right.Length)
                return left;
            else if (left.Length < right.Length)
                return right;
            else
                return left.CompareTo(right) >= 0 ? left : right;
        }

        static string Solve(int digit, int remain, string[,] memo, int[] usable)
        {
            if (memo[digit, remain] != null)
                return memo[digit, remain];
            if (digit <= 0)
                return remain == 0 ? "" : "/";

            if (Array.Exists(usable, x => x == digit) && remain >= Matches[digit])
            {
                return memo[digit, remain] =
                    Max(Solve(digit - 1, remain, memo, usable),
                        digit.ToString() + Solve(digit, remain - Matches[digit], memo, usable));
            }
            else
            {
                return memo[digit, remain] = Solve(digit - 1, remain, memo, usable);
            }
        }

        static void Main(string[] args)
        {
            int n, m;
            ReadInt2(out n, out m);
            int[] A = Console.ReadLine().Split().Select(s => int.Parse(s)).ToArray();

            string[,] memo = new string[10, n + 1];
            string ans = Solve(9, n, memo, A);
            Console.WriteLine(ans);
        }
    }
}