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: Wrong Answer)

(N, M), As = readlines.map{|l| l.split.map(&:to_i)}

h = [*1 .. 9].zip([2, 5, 5, 4, 5, 6, 3, 7, 6]).select{|f, n| As.member?(f)}.to_h
fs = h.keys.sort.reverse
ns = fs.map{|f| h[f]}
dp = Array.new(N + 1, -Float::INFINITY)
dp[0] = 0
(1 .. N).each do |i|
  ns.each{|n| dp[i] = [dp[i], dp[i - n] + 1].max if i - n >= 0}
end
n = N
res = dp[N].times.inject("") do |r, _|
  f = fs.find{|x| dp[n - h[x]] == dp[n] - 1}
  n -= h[f]
  r + f.to_s
end
puts res