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)

AMO = [nil,2,5,5,4,5,6,3,7,6]

N, M = gets.split.map!{|n| n.to_i}

x = gets.split.map!{|n| n.to_i}
a = Hash.new(0)
for i in 1..M
    a[AMO[x[i-1]]] = x[i-1]
end

a = a.to_a

dp = Array.new(N+1)
dp[0] = 0
for i in 1..N
    dp[i] = -1
    a.each do |b|
        if i - b[0] >= 0 && dp[i-b[0]] != -1 && dp[i] < dp[i-b[0]] + 1
            dp[i] = dp[i-b[0]] + 1
        end
    end
end

a.sort!{|a, b| -a[1] <=> -b[1]}
k = N
j = 0
ans = ""

while k != 0 do
    if k - a[j][0] < 0
        j += 1
        next
    end

    if dp[k] == dp[k - a[j][0]] + 1
        ans += a[j][1].to_s
        k -= a[j][0]
    else
        j += 1
    end
end

puts ans