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.chomp.split.map(&:to_i)
NUM=[0,2,5,5,4,5,6,3,7,6]
A = gets.chomp.split.map(&:to_i).sort.reverse

dp = Array.new(N+1, -Float::INFINITY)
dp[0] = 0
1.upto(N) do |i|
  A.each do |a|
    if i - NUM[a] >= 0
      if dp[i] < dp[i - NUM[a]] + 1
        dp[i] = dp[i - NUM[a]] + 1
      end
    end
  end
end

n = N
ans = []
while(n > 0)
  A.each do |a|
    next if n - NUM[a] < 0
    if dp[n - NUM[a]] == dp[n] - 1
      n -= NUM[a]
      ans << a
      break
    end
  end
end

puts ans.map(&:to_s).join