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 Training20200528.Questions;
using Training20200528.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Training20200528.Questions
{
    /// <summary>
    /// https://atcoder.jp/contests/abc118/tasks/abc118_d
    /// </summary>
    public class QuestionF : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nm = inputStream.ReadIntArray();
            var matches = nm[0];
            var availableNumerics = inputStream.ReadIntArray();
            var maxDigits = GetMaximumDigits(matches, availableNumerics);

            yield return GetMaximumInteger(availableNumerics, maxDigits);
        }

        string GetMaximumInteger(int[] availableNumerics, int[] maxDigits)
        {
            Array.Sort(availableNumerics);
            Array.Reverse(availableNumerics);

            var result = new List<int>();

            int match = maxDigits.Length - 1;
            while (match > 0)
            {
                foreach (var current in availableNumerics)
                {
                    var used = GetNeededMatches(current);
                    if (match >= used && maxDigits[match - used] == maxDigits[match] - 1)
                    {
                        match -= used;
                        result.Add(current);
                        break;
                    }
                }
            }

            return string.Concat(result);
        }

        int[] GetMaximumDigits(int matches, int[] availableNumerics)
        {
            var neededMatches = availableNumerics.Select(GetNeededMatches).Distinct().ToArray();
            var maxDigits = Enumerable.Repeat(-(1 << 20), matches + 1).ToArray();
            maxDigits[0] = 0;

            for (int i = 0; i < maxDigits.Length; i++)
            {
                foreach (var neededMatch in neededMatches)
                {
                    if (i + neededMatch < maxDigits.Length)
                    {
                        maxDigits[i + neededMatch] = Math.Max(maxDigits[i + neededMatch], maxDigits[i] + 1);
                    }
                }
            }

            return maxDigits;
        }

        int GetNeededMatches(int n)
        {
            switch (n)
            {
                case 1:
                    return 2;
                case 2:
                    return 5;
                case 3:
                    return 5;
                case 4:
                    return 4;
                case 5:
                    return 5;
                case 6:
                    return 6;
                case 7:
                    return 3;
                case 8:
                    return 7;
                case 9:
                    return 6;
                default:
                    throw new ArgumentOutOfRangeException();
            }
        }
    }
}


namespace Training20200528
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionF();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Training20200528.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Training20200528.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion