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.Linq;
using System.Collections.Generic;

using E = System.Linq.Enumerable;

public class Program
{
    public static void Main()
    {
        var nm = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        var n = nm[0];
        var m = nm[1];
        var nums = Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();
        Array.Sort(nums);
        Array.Reverse(nums);

        var needs = new [] { int.MaxValue, 2, 5, 5, 4, 5, 6, 3, 7, 6 };
        var dp = new int[n + 1];
        var head = 0;
        for (int i = 1; i < dp.Length; i++)
        {
            dp[i] = int.MinValue;
            for (int j = 0; j < nums.Length; j++)
            {
                var r = i - needs[nums[j]];
                if (r < 0)
                {
                    continue;
                }

                if (dp[i] < dp[r] + 1)
                {
                    dp[i] = dp[r] + 1;
                    head = nums[j];
                }
            }
        }
        var repeater = nums.OrderBy(x => needs[x]).First();
        var repeatingLength = Math.Max(0, dp[n] - 2) * needs[repeater];
        var filler = 0;
        for (int i = 0; i < nums.Length; i++)
        {
            var r = n - needs[head] - repeatingLength - needs[nums[i]];
            if (r != 0)
            {
                continue;
            }

            if (filler < nums[i])
            {
                filler = nums[i];
            }
        }

        var middle = new string((char)('0' + repeater), Math.Max(0, dp[n] - 2));
        var tail = filler > 0 ? filler.ToString() : "";
        if (repeater < filler)
        {
            var t = middle;
            middle = tail;
            tail = t;
        }
        Console.WriteLine(head + middle + tail);
    }
}