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)

# util functions

# debug
$debugFlag = ( ARGV[0] != nil )
p "==== DEBUG MODE ====" if $debugFlag

def pd(str)
  p str if $debugFlag
end

def printd(str)
  print str if $debugFlag
end

# input
inputs = []
lc = 0
while l = $stdin.gets do
  if false
    inputs << l.chomp.split(" ").map(&:to_s)
  else
    inputs << l.chomp.split(" ").map(&:to_i)
  end
  lc += 1
end

nn = inputs[0][0]
mm = inputs[0][1]
arr = inputs[1]

# input check
if $debugFlag
  p "--- INPUT (begin) ---"
  inputs.each do |l_i|
    p l_i
  end
  p "--- INPUT (end) ---"
  print "\n"
end

# body
if $debugFlag
  p nn
  p mm
  p arr
end

match = [0,2,5,5,4,5,6,3,7,6]

dp = [0]
for i in 1..nn do
  tmp_max = 0
  for j in 0..arr.size-1 do
    if i - match[arr[j]] > 0 and dp[i - match[arr[j]]] > 0
      cur = dp[i - match[arr[j]]] * 10 + arr[j]
      tmp_max = cur if cur > tmp_max
      cur = dp[i - match[arr[j]]] + arr[j]*(dp[i - match[arr[j]]].to_s(10).length-1)
      tmp_max = cur if cur > tmp_max 
    end
    tmp_max = arr[j] if i == match[arr[j]] and arr[j] > tmp_max
    pd "i=#{i}, j=#{j}, tmp_max=#{tmp_max}"
  end
  dp[i] = tmp_max
  pd dp
end

pd dp
puts dp[-1]