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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;



namespace CSharpSample01
{

    struct Match
    {
        public int v;
        public int m;
    }

    class Program
    {
        
        
        static string DP(int N, Match[] match)
        {
            //dp[i] := i本のマッチをちょうど使う時に作れる最大値文字列
            //dp[i] := ""だと i本のマッチをちょうど使いきれない
            string[] dp = new string[N + 1];
            for (int i = 0; i <= N; i++) dp[i] = "";

            int min = 100;
            foreach(var s in match)
            {
                if (min > s.m) min = s.m;
                if (s.m <= N)
                {
                    dp[s.m] = s.v.ToString();
                }
            }
            
            
            //dp更新処理
            for (int i = 1; i <= N; i++)
            {
                for(int j = 0; j < match.Length; j++)
                {
                    if(i - match[j].m >= 0 && dp[i - match[j].m] != "")
                    {
                        dp[i] = dp[i - match[j].m] + match[j].v.ToString();
                        break;
                    }
                }
            }

            //N本のマッチをちょうど使う時に作れる最大値文字列を返す
            return dp[N];
        }
              
        static void Main(string[] args)
        {
            //N, K, Aの入力
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int M = int.Parse(input[1]);
            int[] a = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();

            //table[i] := 数字iに必要なマッチの本数
            int[] table = { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };

            //使えるマッチの数字と必要な本数
            Match[] match = new Match[a.Length];
            for(int i = 0; i < a.Length; i++)
            {
                match[i] = new Match() { v = a[i], m = table[a[i]] };
            }

            match = match.OrderBy(x => x.m).ThenByDescending(x => x.v).ToArray();


            //DPを解く
            string dprec = DP(N, match);
            dprec = string.Join("", dprec.OrderByDescending(x => x));
            Console.WriteLine(dprec);

        }
    }
}