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;

namespace Algorithm
{
    class Program
    {
        const string MINUSINF = "-";
        static long[] match = new long[] { 2, 5, 5, 4, 5, 6, 3, 7, 6 };
        static string[] dp = Enumerable.Repeat("-", 11000).ToArray();
        static void Main(string[] args)
        {
            // 写経
            var NM = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var A = Console.ReadLine().Split().Select(int.Parse).ToList();

            dp[0] = "";

            for (var i = 0; i <= NM[0]; i++)
            {
                if (dp[i] == MINUSINF) continue;
                foreach (var a in A)
                    ChMax(ref dp[i + match[a - 1]], dp[i] + (char)('0' + a));
            }
            Console.WriteLine(dp[NM[0]]);
        }

        static void ChMax(ref string a, string b)
        {
            if (a == MINUSINF) a = b;
            else if (a.Length < b.Length) a = b;
            else if (a.Length == b.Length)
            {
                if (a.CompareTo(b) < 0) a = b;
            }
        }
    }
}