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

num = {}
[0, 2, 5, 5, 4, 5, 6, 3, 7, 6].each_with_index{|i, idx| num[idx.to_s] = i }

INF = 1e8.to_i
dp = Array.new(n+1, -INF)
dp[0] = 0

for i in 1..n
    maxcol = -INF
    for aj in a
        num_aj = num[aj]

        next if i - num_aj < 0

        if dp[i - num_aj] + 1 > maxcol
            maxcol = dp[i - num_aj] + 1
        end
    end

    if maxcol > 0
        dp[i] = maxcol
    end
end

a = a.sort.reverse
match = n
remcol = dp[n]
ans = ""
while match > 0
    for ai in a
        num_ai = num[ai]

        next if match - num_ai < 0

        if dp[match - num_ai] == remcol - 1
            ans += ai
            remcol -= 1
            match -= num_ai
            break
        end
    end
end

puts ans