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,*A = `dd`.split.map &:to_i
Matches = [ 0, 2, 5, 5, 4, 5, 6, 3, 7, 6 ]
ah = {}
B = A.sort.reverse.map{ |a| ah[Matches[a]] ? nil : a.tap{ |a| ah[Matches[a]] = 1 } }.compact
C = B + [0]

def compare(xh,yh)
  if xh[0] != yh[0]
    return xh[0] > yh[0]
  end
  i = B.index{ |a| xh[a] != yh[a] }
  i ? xh[B[i]] > yh[B[i]] : false
end

dp = (0..N).map{ Hash[C.map{ |a| [a,0] }] }
(0...N).each{ |i|
  next if i > 0 && dp[i][0] == 0
  B.each{ |a|
    n = Matches[a]
    next if i+n > N
    d = dp[i].clone
    d[a] += 1
    d[0] += 1
    if compare(d, dp[i+n])
      dp[i+n] = d
    end
  }
  #p [i, dp[i]]
}
puts B.map{ |a| a.to_s * (dp[N][a] || 0) }.join