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.IO;
using System.Linq;

namespace ABC118D_2
{
    // ABC118Dを漸化式で解く
    class Program
    {
        private static readonly int[] requiredMatches = { 2, 5, 5, 4, 5, 6, 3, 7, 6 };

        static void Main(string[] args)
        {
            if (args.Length > 0)
            {
                Console.SetIn(new StreamReader(args[0]));
            }

            new Program().Solve();
        }

        void Solve()
        {
            var temp = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var numMatches = temp[0];
            var numNumbers = temp[1]; // 使わない
            var availableNumbers = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var maxNumber = new string[numMatches + 1];

            for (int i = 0; i <= numMatches; i++)
            {
                maxNumber[i] = "";

                foreach (int candidate in availableNumbers)
                {
                    if (i < requiredMatches[candidate - 1])
                    {
                        // マッチが足りない場合はスキップ
                        continue;
                    }

                    if (maxNumber[i - requiredMatches[candidate - 1]] == "")
                    {
                        // 最初の数字はマッチを使い切るように置く
                        if (i != requiredMatches[candidate - 1])
                        {
                            continue;
                        }
                    }

                    maxNumber[i] = GetMax(candidate + maxNumber[i - requiredMatches[candidate - 1]], maxNumber[i]);
                }

                Console.Error.WriteLine(i + " : " + maxNumber[i]);
            }

            Console.WriteLine(maxNumber[numMatches]);
        }

        string GetMax(string a, string b)
        {
            if (a.Length > b.Length)
            {
                return a;
            }
            else if (a.Length < b.Length)
            {
                return b;
            }
            else
            {
                return a.CompareTo(b) > 0 ? a : b;
            }
        }
    }
}