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 ABC118D2
{
    class MainClass
    {
        static int[] s;
        static int[] a;
        static int[] dp;
        static int[] w = new int[10] { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };

        public static void Main(string[] args)
        {

            s = Array.ConvertAll(Console.ReadLine().Split().ToArray(), int.Parse);
            a = Array.ConvertAll(Console.ReadLine().Split().ToArray(), int.Parse);

            Array.Sort(a, delegate (int x, int y)
            {
                return w[x].CompareTo(w[y]);
            });

            dp = new int[s[0]+1];
            int digit = Dp(s[0]);
            //Console.WriteLine(digit);
//            Array.Sort(a, delegate (int x, int y){return y.CompareTo(x);});

            string ans = "";
            int weight = s[0];
            for (int i = 0; i < digit; i++)
            {

                for(int j = 0; j < s[1]; j++)
                {
                    if (weight - w[a[j]] >= 0)
                    {
                        //Console.WriteLine("weight: " + weight + " a[j]: " + a[j]);
                        if (Dp(weight) == Dp(weight- w[a[j]]) + 1)
                        {
                            ans += a[j].ToString();
                            weight -= w[a[j]];
                            //Console.WriteLine("assigned");
                            break;
                        }
                        else
                        {
                            //Console.WriteLine("skipped");
                        }
                    }

                }
            }

            Console.WriteLine(ans);




        }



        public static int Dp(int m)
        {
            //Console.WriteLine(m);
            if (m == 0) {
                return 0;
            }

            if (dp[m] != 0)//calcurated
            {
                return dp[m];
            }
            else
            {
                int M = s[1];
                int tmp = -1;
                int ans = -1;
                for (int i = 0; i < M; i++)
                {
                    int dptmp = m - w[a[i]];
                    if (dptmp >= 0)
                    {
                        tmp = Dp(dptmp) + 1;
                    }
                    ans = Math.Max(ans, tmp);
                }
                dp[m] = ans;
                return ans;
            }
        }
    }
}