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 = gets.split.map(&:to_i)
b = [0,2,5,5,4,5,6,3,7,6]
a = gets.split.map(&:to_i)
for i in 0..m-1
    for j in 0..m-1
        next if i == j
        if b[a[i]] == b[a[j]]
            a[i],a[j] = a[j],a[i] if a[i] < a[j]
            a[j] = 0
        end
    end
end
a.delete(0)
a.sort_by!{|i|b[i]}
t = a.size
c = Array.new(t){|i|b[a[i]]}
dp = Array.new(n+1,0)
s = Array.new(n+1).map{Array.new(t,0)}
n.times do |i|
    next if dp[i] == 0 && i != 0
    t.times do |j|
        break if i+c[j] > n
        if dp[i+c[j]] <= dp[i]+1
            dp[i+c[j]] = dp[i]+1
            s[i+c[j]] = Marshal.load(Marshal.dump(s[i]))
            s[i+c[j]][j] += 1
        end
    end
end
ans = []
t.times do |i|
    s[n][i].times do
        ans << a[i]
    end
end
puts ans.sort.reverse.join("")