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)
usable = [] # usable[i]: 数字iを使えるかどうか
A.each { |a| usable[a] = true }
nums = [1, 7, 4, 5, 3, 2, 9, 6, 8] # マッチの本数順にソートされた数字
mnums = [nil, 2, 5, 5, 4, 5, 6, 3, 7, 6] # mnums[i]: 数字iのマッチの本数
dp = Array.new(N + 1, -999) # dp[i]: i本のマッチをちょうど使ってできる最大桁数

dp[0] = 0
1.upto(N) do |i|
  nums.each do |num|
    next if !usable[num] || i < mnums[num]
    dp[i] = [dp[i], dp[i - mnums[num]] + 1].max
  end
end

n = N
dp.last.times do
  9.downto(1).each do |num|
    if usable[num] && n >= mnums[num] && dp[n - mnums[num]] == dp[n] - 1
      n -= mnums[num]
      print num
      break
    end
  end
end

puts