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;
using System.Collections.Generic;
using System.Text;


public class D
{	
	public static void Main()
	{
		string[] args;
		args = Console.ReadLine().Split(' ');
		int N = Int32.Parse(args[0]);
		int M = Int32.Parse(args[1]);
		
		List<int> A = new List<int>(M);
		args = Console.ReadLine().Split(' ');
		for(int i = 0; i < M; i++)
			A.Add(Int32.Parse(args[i]));
		A.Sort((x,y) => y - x);
		
		int[] num = {-1,2,5,5,4,5,6,3,7,6};
		
		int[] dp = new int[N + 1];		
		dp[0] = 0;		
		for(int i = 1; i <= N; i++)
			dp[i] = -1000000000;
		
		for(int i = 1; i <= N; i++)
		{
			for(int j = 0; j < M; j++)
			{
				if(i < num[A[j]])
					continue;
				dp[i] = Math.Max(dp[i], dp[i - num[A[j]]] + 1);
			}				
		}
		
		StringBuilder sb = new StringBuilder();
		int rest = N;
		for(int i = 0; i < dp[N]; i++)
		{
			for(int j = 0; j < M; j++)
			{
				if(rest < num[A[j]])
					continue;
				if(dp[rest - num[A[j]]] != dp[rest] - 1)
					continue;
				sb.Append(A[j].ToString());
				rest -= num[A[j]];
				break;
			}			
		}
		
		Console.WriteLine(sb);		
	}
}