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: Time Limit Exceeded)

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

MIN = A.map do |a|
  COSTS[a]
end.min

# dp[i]: マッチをi本使ったときの最大の桁数
# dp[i] = max(dp[i - COSTS(A[j])] + 1| j = 1 ~ M)
dp = Array.new(N + 1) {0}

dp[0] = 0
1.upto(MIN-1) do |i|
  dp[i] = nil
end
MIN.upto(N) do |i|
  dp[i] = i / MIN
end

ans = ''
remaining = dp[N]
match = N

# 大きい桁から決めていく
while match > 0
  # p "match #{match} remaining #{remaining}"
  A.each do |a|
    if match - COSTS[a] < 0
      next
    end

    if dp[match - COSTS[a]].nil?
      next
    end

    # p "a: #{a} digit: #{dp[match - COSTS[a]]} from #{match - COSTS[a]}"

    if dp[match - COSTS[a]] + 1 == remaining
      # p "choose #{a}"
      ans = ans + a.to_s
      match -= COSTS[a]
      remaining -= 1
      break
    end
  end
end

puts ans