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 ABC118
{
    public class D
    {
        int INF = 1000000000;
        public void Solve()
        {
            string[] s = Console.ReadLine().Split(' ');
            int N = int.Parse(s[0]);
            int M = int.Parse(s[1]);
            int[] A = new int[M];
            string[] As = Console.ReadLine().Split(' ');
            for (int i = 0; i < M; i++) { A[i] = int.Parse(As[i]); }
            A = A.OrderByDescending(x => x).ToArray();

            int[] dp = new int[N + 1];
            dp[0] = 0;
            int[] num = new int[9] {2, 5, 5, 4, 5, 6, 3, 7, 6};

            for (int i = 1; i < N + 1; i++)
            {
                int max = -INF;
                for (int j = 0; j < A.Length; j++)
                {
                    if (i - num[A[j] - 1] >= 0)
                    {
                        max = Max<int>(max, dp[i - num[A[j] - 1]] + 1);
                    }
                }
                dp[i] = max;
            }
            int Nc = N;
            for (int i = 0; i < dp[N]; i++)
            {
                for (int j = 0; j < A.Length; j++)
                {
                    if (Nc - num[A[j] - 1] >= 0 && dp[Nc - num[A[j] - 1]] == dp[Nc] - 1)
                    {
                        Console.Write("{0}", A[j]);
                        Nc -= num[A[j] - 1];
                        break;
                    }
                }
            }
            Console.Write("\n");
        }

        T Min<T>(params T[] nums) where T : IComparable
        {
            if (nums.Length == 0) { return default(T); }

            T min = nums[0];
            for (int i = 0; i < nums.Length; i++) { min = (min.CompareTo(nums[i]) < 0) ? min : nums[i]; }

            return min;
        }

        T Max<T>(params T[] nums) where T : IComparable
        {
            if (nums.Length == 0) { return default(T); }

            T max = nums[0];
            for (int i = 0; i < nums.Length; i++) { max = (max.CompareTo(nums[i]) > 0) ? max : nums[i]; }

            return max;
        }
    }
}

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new ABC118.D().Solve();
        }
    }
}