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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

static class CodeJam
{
    static bool GreaterThan(string a, string b)
    {
        return (a.Length == b.Length) ? (a.CompareTo(b) > 0) : (a.Length > b.Length);
    }

    static string Solve(int N, int[] A)
    {
        int[] C = { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };

        var dp = new string[N + 1];
        dp[0] = "";
        for (int i = 0; i < N; ++i)
        {
            if (dp[i] != null)
            {
                foreach (int a in A)
                {
                    int key = i + C[a];
                    if (key <= N)
                    {
                        string value = a.ToString() + dp[i];
                        if (dp[key] == null || GreaterThan(value, dp[key]))
                        {
                            dp[key] = value;
                        }
                    }
                }
            }
        }
        return dp[N];
    }

    static void Main(string[] args)
    {
        int[] V = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int[] A = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        Console.WriteLine(Solve(V[0], A));
    }
}