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;

class Program
{
    static void Main(string[] args)
    {
        var nm = Console.ReadLine().Split();
        var n = int.Parse(nm[0]);
        var m = int.Parse(nm[1]);

        var A = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

        var dp = new string[n + 1];
        dp[0] = "";
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                if (i + 1 < nums(A[j])) continue;
                if (dp[i + 1 - nums(A[j])] == null) continue;

                dp[i + 1] = max(dp[i + 1], dp[i + 1 - nums(A[j])] + A[j]);
            }
        }

        Console.WriteLine(dp[n]);
    }

    static string max(string x, string y)
    {
        if (x == null) return y;
        if (y == null) return x;
        if (x.Length < y.Length) return y;
        if (y.Length < x.Length) return x;

        if (0 < x.CompareTo(y))
        {
            return x;
        }
        else
        {
            return y;
        }
    }

    static int[] _nums = new[] { 2, 5, 5, 4, 5, 6, 3, 7, 6 };
    static int nums(int n)
    {
        return _nums[n - 1];
    }
}