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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.List (intersect, sortBy)
import qualified Data.IntMap as M
import Data.Function (on)

main :: IO ()
main = do
  n <- read . head . words <$> getLine
  as <- map read . words <$> getLine
  let
      ps = map (id >< head) $ filter (not . null . snd) $ map (id >< (intersect as)) priority
      ps' = M.fromAscList ps
      js = map fst $ reverse $ sortBy (compare `on` snd) ps -- descending
      j' = last js
      n' = n `div` j'
      dp = M.fromAscList $ map ((,) <$> id <*> f) [0..n']
      f 0 = [(0, [])]
      f i = do
        j <- js
        (s, r) <- dp M.! (pred i)
        if j + s <= n then return (j + s, j : r) else []
      ls = foldr (\a b-> if fst a == n then snd a else b) [] $ reverse [0..n'] >>= (M.!) dp
      v = foldl (\a j -> 10 * a + (ps' M.! j)) 0 ls
  print v

priority = [(2, [1]), (3, [7]), (4, [4]), (5, [5, 3, 2]), (6, [9, 6]), (7, [8])]

(f >< g) (x, y) = (f x, g y)
infixr 5 ><