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.Linq;
using System.Collections.Generic;
class P
{
    static int[] s = { 2, 5, 5, 4, 5, 6, 3, 7, 6 };
    static void Main()
    {
        var inputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int n = inputs[0], m = inputs[1];
        var a = Console.ReadLine().Split().Select(int.Parse).ToArray();
        bool[] e = new bool[9];
        foreach (var i in a)
            e[i - 1] = true;
        HashSet<int> hs = new HashSet<int>();
        for (int i = 1; i <= 9; i++)
            if (a.Contains(i))
                hs.Add(s[i - 1]);
        var dp = new int[n + 1];
        for (int i = 1; i <= n; i++)
            dp[i] = -int.MaxValue;
        for (int i = 1; i <= n; i++)
        {
            for (int j = 0; j < 9; j++)
            {
                if (!e[j])
                    continue;
                try
                {
                    dp[i] = Math.Max(dp[i], dp[i - s[j]] + 1);
                }
                catch { }
            }
        }
        List<int> ans = new List<int>();
        for (int i = 8; i >= 0; i--)
        {
            if (!e[i])
                continue;
            while (true)
            {
                    if (n >= s[i] && dp[n - s[i]] + 1 == dp[n])
                    {
                        ans.Add(i + 1);
                        n -= s[i];
                    }
                    else
                    {
                        break;
                    }
            }
            if (n == 0)
                break;
        }
        foreach (var i in ans)
            Console.Write(i);
        Console.WriteLine();
    }
}