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.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>();
		foreach(var v in split){
			rule2.Add(rule[v-1],v);
		}
		var dp_dic = new Dictionary<int,int>();
		dp_dic.Add(0,0);
		foreach(var loop in Enumerable.Range(1,n)){
			foreach(var d in rule2.OrderByDescending(x=>x.Value)){
				if(dp_dic.Keys.Contains(loop-d.Key)){
					if(dp_dic[loop-d.Key]==int.MinValue)continue;
					if(dp_dic.Keys.Contains(loop)){
						if(dp_dic[loop]<dp_dic[loop-d.Key]+1){
							dp_dic[loop] = dp_dic[loop-d.Key]+1;
						}
						continue;
					}
					dp_dic.Add(loop,dp_dic[loop-d.Key]+1);
				}
			}
			if(!dp_dic.Keys.Contains(loop)){
				dp_dic.Add(loop,int.MinValue);
			}
		}
		while(n>0){
			foreach(var d in rule2.OrderByDescending(x=>x.Value)){
				if(n-d.Key<0)continue;
				if(dp_dic[n-d.Key]==dp_dic[n]-1){
					Console.Write(d.Value);
					n-=d.Key;
					break;
				}
			}
		}
		Console.WriteLine();
	}
	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);
		}
	}
}