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: Runtime Error)

N,M = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)
b = [0,2,5,5,4,5,6,3,7,6]

a.sort_by!{|v| [b[v],-v]}
c,d = a[0],b[a[0]]
dp = []*(N+1)
dp[0] = 0

1.upto(N) do |i|
  tmp = []
  a.each do |v|
    tmp << dp[i-b[v]] + 1 if i >= b[v] && !dp[i-b[v]].nil?
  end
  dp[i] = tmp.empty? ? nil : tmp.max
end

ans = c.to_s*dp[N]
ex = N - dp[N] * d

a.sort!.reverse!
l,r = 0,ans.length
a.each do |v|
  diff = b[v]-d
  if ex >= diff && v > c
    cnt = ex/diff
    ans[l,cnt] = v.to_s * cnt
    l += cnt
    ex %= diff
  end
end
a.sort_by!{|v| [-b[v],-v]}
a.each do |v|
  diff = b[v]-d
  if ex >= diff && v < c
    cnt = ex/diff
    ans[r-cnt,cnt] = v.to_s * cnt
    r -= cnt
    ex %= diff
  end
end
puts ans