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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
using System.Numerics;

namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            Solve();
            //Out.Flush();
            Read();
        }

        static void Solve()
        {
            var (N, M) = Slice2<int>();
            Ai = Sarray();
            if (Ai.Contains(2) && (Ai.Contains(3) || Ai.Contains(5))) Ai = Ai.Where(a => a != 2).ToArray();
            if (Ai.Contains(3) && Ai.Contains(5)) Ai = Ai.Where(a => a != 3).ToArray();
            if (Ai.Contains(6) && Ai.Contains(9)) Ai = Ai.Where(a => a != 6).ToArray();
            ktNum = new int[10];
            //最大桁数が出る
            ktDfs(N, 1);
            var keta = ktNum.Sum();

            mxNum = new int[10];
            bsN = odNum.Select((o, i) => (idx: i , num: o)).Where(o => Ai.Contains(o.idx)).OrderBy(oi => oi.num).First().idx;
            var bCst = odNum[bsN];
            odNum = odNum.Select(o => o - bCst).ToArray();
            mxDfs(N - bCst * keta, 9);
            var ans = string.Empty;
            mxNum[bsN] = keta - mxNum.Sum();
            for (var i = 9; 0 <= i; --i)
                ans += new String((char)(i + '0'), mxNum[i]);
            WriteLine(ans);
        }
        static long[] Ai;
        static int[] prOrd = new int[] { 0, 1, 7, 4, 5, 2, 3, 9, 6, 8 };
        static int[] ktNum;

        static int[] odNum = new int[] { 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 };
        static int[] mxNum;
        static int bsN;
        static bool ktDfs(int rem, int no)
        {
            if (rem == 0) return true;
            if (9 < no) return false;
            if (rem < 0) return false;
            var num = prOrd[no];
            if (!Ai.Contains(num)) return ktDfs(rem, no + 1);
            for (var i = rem / odNum[num]; 0 <= i; --i)
            {
                ktNum[num] = i;
                if (ktDfs(rem - i * odNum[num], no + 1)) return true;
            }
            return false;
        }
        static int sig = -1;
        static bool mxDfs(int rem, int no)
        {
            if (rem == 0) return true;
            if (sig < 0 && no == bsN) { sig = 1; no = 1; }
            if (0 < sig && no == bsN) return false;
            if (!Ai.Contains(no)) return mxDfs(rem, no + sig);

            for (var i = rem / odNum[no]; 0 <= i; --i)
            {
                var psig = sig;
                mxNum[no] = i;
                if (mxDfs(rem - i * odNum[no], no + sig)) return true;
                sig = psig;
            }
            return false;
        }

        static long Mod = 998244353;
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }
        static public (T1 a, T2 b) Slice<T1, T2>()
        {
            var t = ReadLine().Split();
            return (
            (T1)Convert.ChangeType(t[0], typeof(T1)),
            (T2)Convert.ChangeType(t[1], typeof(T2)));
        }
        static public (T a, T b) Slice2<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)));
        }
        static public (T a, T b, T c) Slice3<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)),
            (T)Convert.ChangeType(t[2], typeof(T)));
        }
        static public (T a, T b, T c, T d) Slice4<T>()
        {
            var t = ReadLine().Split();
            return (
            (T)Convert.ChangeType(t[0], typeof(T)),
            (T)Convert.ChangeType(t[1], typeof(T)),
            (T)Convert.ChangeType(t[2], typeof(T)),
            (T)Convert.ChangeType(t[3], typeof(T)));
        }
    }
}