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: Accepted)

import qualified Data.Text as T
import qualified Data.Text.IO as T
import qualified Data.Text.Read as T
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import Data.List (sortBy)
import Data.Maybe (fromJust)

main :: IO ()
main = do
  [n, m] <- map unsafeTextToInt . T.words <$> T.getLine :: IO [Int]
  as <- sortBy (flip compare) . map unsafeTextToInt . T.words <$> T.getLine :: IO [Int]
  let
    table = V.constructN (succ n) rec :: V.Vector (Maybe (Int, [Int]))
      where
        rec :: V.Vector (Maybe (Int, [Int])) -> (Maybe (Int, [Int]))
        rec v | l == 0    = Just (0, [])
              | otherwise = maximum . map f $ as
          where
            l = V.length v :: Int
            f :: Int -> Maybe (Int, [Int])
            f d | l < k     = Nothing
                | otherwise = ((,) <$> succ . fst <*> (d :) . snd) <$> v V.! (l - k)
              where
                k = matchNums VU.! d :: Int
  mapM_ (putStr . show) . snd . fromJust $ table V.! n
  putStrLn ""

matchNums = VU.fromList [6, 2, 5, 5, 4, 5, 6, 3, 7, 6] :: VU.Vector Int
{-# INLINE matchNums #-}

unsafeTextToInt :: T.Text -> Int
unsafeTextToInt s = case T.signed T.decimal s of
  Right (n, _) -> n
{-# INLINE unsafeTextToInt #-}