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;

class Dmondai {
    static void Main()
    {
        var line = Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).ToArray();
        var N = line[0];
        var M = line[1];
        //使える数字
        var A= Console.ReadLine().Split(' ').Select(x => Int32.Parse(x)).OrderByDescending(x=>x).ToArray();
        //それぞれの数字で使用するマッチの本数（index+1=数字）
        var cost = new int[] { 2,5,5,4,5,6,3,7,6};
        //dp用の配列
        var dp = new int[N+1];
        //マッチ棒を0本使用してできる桁はないので、0を入れる
        dp[0] = 0;
        //dpの配列にintの最小の数を入れる（inde=0以外）
        for (int i = 1; i <= N; ++i) dp[i] = int.MinValue;
        //動的計画法
        //マッチ棒をdpのindexぶん、使ったときにできる最大桁数を求める
        for (int i=0;i<=N;++i)
        {
            if (i != 0 && dp[i] == int.MinValue) continue;
            for (int j=0;j<M;++j)
            {
                if (N < i + cost[A[j] - 1]) continue;
                dp[i+cost[A[j] - 1]] = dp[i]+1;
            }
        }
        //答えを格納する文字列を用意
        var ans = string.Empty;
        //数字の文字列を作成する
        var index = N;
        while (0<index)
        {
            for (int j=0;j<M;++j)
            {
                if (index - cost[A[j] - 1] < 0) continue;
                if (dp[index - cost[A[j] - 1]] == dp[index] -1) {
                    ans += A[j];
                    index -= cost[A[j] - 1];
                    break;
                }
            }
        }
        Console.WriteLine(ans);
    }
}