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: Time Limit Exceeded)


{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE OverloadedLists #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE TypeFamilies #-}

import GHC.Exts (IsList(..))

import Data.String (IsString)
import Data.Array (Array, array, (!))
import qualified Data.Map as M
import Data.Map (Map, insert)
import Data.Maybe (catMaybes, fromJust)

import Control.Monad (forM_, when)
import Control.Monad.Trans.Class (lift)
import Control.Monad.Trans.State.Strict (State, get, modify, execState)
import Control.Monad.Trans.Reader (ReaderT(..), ask)

newtype StrNum = StrNum String deriving (Eq, IsString)

instance IsList StrNum where
  type Item StrNum = Char
  fromList = StrNum
  toList (StrNum s) = s

instance Show StrNum where
  show (StrNum s) = s

instance Ord StrNum where
  compare (StrNum a) (StrNum b)
    | la < lb = LT
    | la > lb = GT
    | la == lb = case compare (head a) (head b) of
                     EQ -> compare (StrNum (tail a)) (StrNum (tail b))
                     c -> c
    where
      la = length a
      lb = length b

match :: Array Char Int
match = array ('1','9') [('1',2),('2',5),('3',5),('4',4),('5',5),('6',6),('7',3),('8',7),('9',6)]

cons :: Char -> StrNum -> StrNum
cons c (StrNum s) = StrNum (c:s)

main :: IO ()
main = do
  n <- read . head . words <$> getLine :: IO Int
  as <- map head . words <$> getLine
  let dptable = flip execState (M.fromList [(0,"")]) $ flip runReaderT as $ dp n
  print $ fromJust $ M.lookup n dptable

dp :: Int -> ReaderT [Char] (State (Map Int StrNum)) ()
dp 0 = return ()
dp n = do
  dp (n-1)
  table <- lift get
  as <- ask
  let ds = catMaybes [(cons a) <$> M.lookup (n-m) table | a <- as, let m = match ! a]

  when (not $ null ds) (lift $ modify $ insert n $ maximum ds)