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 Ruby (2.3.3) (judge verdict: Accepted)

N, M = gets.split(' ').map(&:to_i)
A = gets.split(' ').map(&:to_i)
grids = [0, 2, 5, 5, 4, 5, 6, 3, 7, 6]

numbers = []
A.each do |n|
  numbers.push([n, grids[n]])
end
numbers.sort_by!{|a| [a[1], -a[0]]}

dp = Array.new(N+1)
dp[0] = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
1.upto(N) do |ma|
  numbers.each do |i|
    next if ma < i[1]
    if dp[ma - i[1]] != nil
      cand = [0] * 10
      1.upto(9) do |l|
        cand[l] = dp[ma - i[1]][l]
      end
      cand[i[0]] = cand[i[0]] + 1
 	  if dp[ma] == nil
        dp[ma] = cand
      else
        mx = true
        mx = false if dp[ma].inject(:+) > cand.inject(:+)
        9.downto(1) do |j|
          next if dp[ma][j] == cand[j]
          if dp[ma][j] > cand[j]
            mx = false
            break
          end
          if dp[ma][j] < cand[j]
            break
          end
        end
        dp[ma] = cand if mx
      end
    end
  end
end
ans = ""
9.downto(1) do |i|
  ans = ans + i.to_s * dp[N][i]
end
puts ans