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 OCaml (4.02.3) (judge verdict: Accepted)

let cost = Array.get [| 2; 5; 5; 4; 5; 6; 3; 7; 6 |]

let () = Scanf.scanf "%d %d" @@ fun n m ->
  let as_ = Array.init m @@ fun m -> Scanf.scanf "%c%d" @@ fun _ a -> a in
  let dp = Array.make (n + 10) (-1, []) in
  dp.(0) <- (0, []);
  for i = 0 to n - 1 do
    Array.iter (fun a ->
      if 0 <= fst dp.(i) then
        dp.(i + cost (a - 1)) <-
          max dp.(i + cost (a - 1)) @@ (fst dp.(i) + 1, a :: snd dp.(i))) as_
  done;
  List.iter print_int (snd dp.(n));
  print_newline ()