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本のマッチをピッタリ使い、mの数字の範囲で最大

waste = {
1 => 2,
2 => 5,
3 => 5,
4 => 4,
5 => 5,
6 => 6,
7 => 3,
8 => 7,
9 => 6,
}

n, m = gets.split.map &:to_i
as = gets.split.map &:to_i

$diff = {}

as.each{ |x|
	if $diff[waste[x]] == nil then
		$diff[waste[x]] = []
	end
	
	$diff[waste[x]] << x
}

$diff.each{ |k, v|
	$diff[k] = v.max
}

$diff_keys = $diff.keys.sort

$lcm = $diff_keys[0]

$diff_keys[1..-1].each{ |x|
	$lcm = $lcm.lcm(x)
} 

$count = Array.new($diff_keys.size, 0)

#p $diff
#p $diff_keys
#p $lcm

$result = []
$digit_count = nil

def ll(remain, idx)
#	puts "remain:" + remain.to_s
#	puts "key:" + $diff_keys[idx].to_s
	start = remain / $diff_keys[idx]
#	puts "start:" + remain.to_s
#	puts
	start.downto([start - $lcm / $diff_keys[idx], 0].max){ |i|
		$count[idx] = i
		next_remain = remain - i * $diff_keys[idx]

		if next_remain == 0 then
			output = []
			$count.each_with_index{ |d, k|
				output << $diff[$diff_keys[k]].to_s * d
			}

			val = output.sort.reverse.join("")

			if $digit_count == nil || $digit_count == val.size then
				$digit_count = val.size
				$result << val.to_i
			else
				puts $result.max
				exit
			end
		end

		if next_remain > 0 && idx < $diff_keys.size - 1 then
			ll(next_remain, idx + 1)
		end
	}
end

ll(n, 0)

puts $result.max