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.Collections.Generic;
using System.Linq;
 
public class Program
{
	public static void Main()
	{
		var rule = new int[]{2,5,5,4,5,6,3,7,6};
		var split = Console.ReadLine().Split().Select(int.Parse).ToList();
		var n = split[0];
		var m = split[1];
		split = Console.ReadLine().Split().Select(int.Parse).ToList();
		Check(split);
		var rule2 = new Dictionary<int,int>();
		var rule_list = new Dictionary<int,List<int>>();
		foreach(var v in split){
			rule2.Add(rule[v-1],v);
			rule_list.Add(rule[v-1],new List<int>{v});
		}
		var min = rule2.Keys.Min();
		var max = n/min;
		if(min*max == n){
			for(int i = 0;i<max;i++){
				Console.Write(rule2[min]);
			}
			Console.WriteLine();
		}
		else {
			var ans = Enumerable.Repeat(rule2[min], max).ToList();
			var ans_list = new List<List<int>>();
			var loop = 1;
			n = (n % min)+min;
			while(ans.Count()>0){
				var next_list = new Dictionary<int,List<int>>();
				foreach(var v in rule_list.Where(x=>x.Key<n&&x.Key>n-min)){
					foreach(var v2 in rule2){
						var tmp = new List<int>(v.Value);
						tmp.Add(v2.Value);
						var n_k = v2.Key+v.Key;
						if(next_list.Keys.Contains(n_k)){
							if(next_list[n_k].Count()<tmp.Count()){
								next_list[n_k]=tmp;
							}else if(next_list[n_k].Count()==tmp.Count()){
								next_list[n_k].Sort((a,b)=>(int)b-(int)a);
								tmp.Sort((a,b)=>(int)b-(int)a);
								for(int count = 0;tmp.Count()>count;count++)
								if(next_list[n_k].Skip(count).ElementAt(0)<tmp.Skip(count).ElementAt(0)){
									next_list[n_k]=tmp;
								}
							}
							continue;
						}
						next_list.Add(n_k,tmp);
					}
				}
				foreach(var v in next_list){
					if(rule_list.Keys.Contains(v.Key)){
						if(rule_list[v.Key].Count() < v.Value.Count()){
							rule_list[v.Key]=v.Value;
						}else if(rule_list[v.Key].Count()==v.Value.Count()){
							rule_list[v.Key].Sort((a,b)=>(int)b-(int)a);
							v.Value.Sort((a,b)=>(int)b-(int)a);
							for(int count = 0;v.Value.Count()>count;count++){
								if(rule_list[v.Key].Skip(count).ElementAt(0)<v.Value.Skip(count).ElementAt(0)){
									rule_list[v.Key]=v.Value;
								}
							}
						}
						continue;
					}
					rule_list.Add(v.Key,v.Value);
				}
				if(rule_list.Keys.Contains(n)){
					if(loop == rule_list[n].Count()){
						ans.AddRange(rule_list[n]);
						PrintAns(ans);
						return;
					}else{
						var ans_tmp = new List<int>(ans);
						ans_tmp.AddRange(rule_list[n]);
						ans_list.Add(ans_tmp);
					}
				}
				ans.RemoveAt(0);
				n = n + min;
				loop++;
			}
			ans = ans_list.OrderBy(x=>x.Count()).OrderBy(x=>x.Max()).ElementAt(0);
			PrintAns(ans);
		}
	}
	public static void Check(List<int> list){
		if(list.Contains(2)&&list.Contains(3)){
			list.Remove(2);
		}
		if(list.Contains(3)&&list.Contains(5)){
			list.Remove(3);
		}
		if(list.Contains(2)&&list.Contains(5)){
			list.Remove(2);
		}
		if(list.Contains(6)&&list.Contains(9)){
			list.Remove(6);
		}
	}
	public static void PrintAns(List<int> ans){
		ans.Sort((a,b)=>(int)b-(int)a);
		foreach(var v in ans){
			Console.Write(v);
		}
		Console.WriteLine();
	}
}