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;

class Program
{

    static void Main(string[] args)
    {
        var inputs = Console.ReadLine().Split(' ');
        var N = int.Parse(inputs[0]);
        var M = int.Parse(inputs[1]);
        var A = new int[M];
        inputs = Console.ReadLine().Split(' ');
        for (int i = 0; i < M; i++)
        {
            A[i] = int.Parse(inputs[i]);
        }

        A = A.OrderByDescending((a) => a).ToArray();

        var countMap = new Dictionary<int, int>();
        int n = 1;
        countMap.Add(n++, 2);
        countMap.Add(n++, 5);
        countMap.Add(n++, 5);
        countMap.Add(n++, 4);
        countMap.Add(n++, 5);
        countMap.Add(n++, 6);
        countMap.Add(n++, 3);
        countMap.Add(n++, 7);
        countMap.Add(n++, 6);

        // dp[i]: i本のマッチを使用して作成できる最大桁数
        var dp = new int[N + 1];
        for (int i = 1; i < dp.Length; i++)
        {
            int max = 0;
            // dp[i] = max_j { dp[i - num(Aj)] + 1 } 
            for (int j = 0; j < M; j++)
            {
                var numj = countMap[A[j]];
                if (i < numj)
                {
                    continue;
                }
                max = Math.Max(dp[i - numj] + 1, max);
            }
            dp[i] = max;
        }

        string ans = string.Empty;
        int match = N;
        int remain = dp[N];
        while (match > 0)
        {
            for (int i = 0; i < M; i++)
            {
                int next = match - countMap[A[i]];
                // 端数処理。next != 0なのでdp[next] = 0となるのは対象が無いのと同じ
                if (next < 0 || (dp[next] == 0 && next != 0))
                {
                    continue;
                }

                // dp[N - num(Ai)] = dp[N] - 1
                // 最大桁から見るとちょうど一桁ずつ減っていく
                // 尚、使いきる場合、next = 0となる
                if (dp[next] == remain - 1 || next == 0)
                {
                    ans += A[i];
                    match -= countMap[A[i]];
                    remain--;
                    break;
                }
            }
        }

        Console.WriteLine(ans);
    }

}