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: Runtime Error)

import Data.List (sort)
import qualified Data.IntMap as M
import Data.List (unfoldr)

main :: IO ()
main = do
  n <- read . head . words <$> getLine
  as <- reverse . sort . map read . words <$> getLine
  let
    ls = (dp M.!)
      where
        dp = M.fromAscList $ map ((,) <$> id <*> f) [0..n]
        f 0 = [0]
        f i = concat . map (map (1 +) . (dp M.!)) . filter (>= 0) . map ((i -) . num) $ as
    l = maximum . (0 :) . ls $ n
    ds = unfoldr (\(i, k) -> foldr (\d r -> if i > 0 && k > 0 && (pred k `elem` ls (i - num d)) then Just (d, (i - num d, pred k)) else r) Nothing as) (n, l)
  print $ foldl (\a i -> 10 * a + i) 0 ds

num = (matches M.!)
  where
    matches = M.fromAscList [(1, 2), (2, 5), (3, 5), (4, 4), (5, 5), (6, 6), (7, 3), (8, 7), (9, 6)]