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)
num = gets.split.map(&:to_i)
num.sort!
stick = [10,2,5,5,4,5,6,3,7,6]
ans = []
check = [0,10]
for i in 0..m-1
  if check[1] >= stick[num[i]]
    check[0] = num[i]
    check[1] = stick[num[i]]
  end
end
num2 = Array.new(7, 0)
for i in 1..m**7
  count = 0
  for j in 0..6
    if num2[j] != 0
      count += stick[num[-num2[j]]]
    end
  end
  if (n - count) % check[1] == 0
    for k in 1..7
      if num2[-k] != 0
        for j in 1..m
          if (stick[num[-num2[-k]]] - stick[num[-j]]) % check[1] == 0 && stick[num[-num2[-k]]] > stick[num[-j]]
            num2[-k] = j
            count -= (stick[num[-num2[-k]]] - stick[num[-j]])
          end
        end
      end
    end
    break
  end
  num2[0] += 1
  for j in 0..5
    if num2[j] == m+1
      num2[j] = 1
      num2[j+1] += 1
    end
  end
end
ans = []
for i in 1..7
  if num2[-i] != 0
    ans.push(num[-num2[-i]])
  end
end
if ans.length != 0
  ans.sort!
end
if ans.length != 0 && ans[0] < check[0]
  for i in 1..((n-count)/check[1])
    ans.insert(0,check[0])
  end
else
  for i in 1..((n-count)/check[1])
    ans.push(check[0])
  end
end
puts ans.join