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 FlexibleContexts #-}
{-# LANGUAGE RankNTypes #-}

import Data.Array (Array, array, (!))
import Data.Array.ST (STArray, MArray, runSTArray, readArray, writeArray, newArray)
import Data.Maybe (fromJust, catMaybes)

import Control.Monad (forM_, when)
import Control.Monad.ST (ST)

newtype NumStr = NumStr {getString :: String} deriving Eq
instance Ord NumStr where
  compare (NumStr s1) (NumStr s2)
    | l1 < l2 = LT
    | l1 > l2 = GT
    | otherwise = case compare (head s1) (head s2) of
                    EQ -> compare (NumStr (tail s1)) (NumStr (tail s2))
                    n -> n
    where
      l1 = length s1
      l2 = length s2

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)]

main :: IO ()
main = do
  n <- read . head . words <$> getLine
  as <- map head . words <$> getLine
  let solv = do
      arr <- initialize n
      forM_ [2..n] $ \i -> dp i as arr
      return arr
  let dptable = runSTArray solv
  putStrLn $ fromJust $ dptable ! n

initialize :: Int -> (forall s. ST s (STArray s Int (Maybe String)))
initialize n = do
  arr <- newArray (0,n) Nothing
  writeArray arr 0 (Just "")
  return arr

dp :: Int -> [Char] -> STArray s Int (Maybe String) -> ST s ()
dp n as arr = do
  ds <- catMaybes <$> sequence [fmap (a:) <$> readArray arr (n - m) | a <- as, let m = match!a, n-m>=0]
  when (not $ null ds) $ 
    writeArray arr n $ Just $ getString $ maximum $ fmap NumStr $ ds