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)


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

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

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

type StrL = (String, Int)
cons x (xs, n) = (x:xs, n+1)

cmp (s1,l1) (s2,l2)
  | l1 < l2 = LT
  | l1 > l2 = GT
  | otherwise = compare s1 s2

match = listArray ('1', '9') [2,5,5,4,5,6,3,7,6]

mm :: [Char] -> Int -> (forall s. ST s (STArray s Int (Maybe StrL)))
mm as n = do
    arr <- newArray (0,n) Nothing
    writeArray arr 0 (Just ("", 0))
    forM_ [2..n] $ \i -> nth arr i >>= writeArray arr i
    return arr
  where
    nth arr i = do
      cands <- fmap catMaybes . sequence $
                [fmap (cons a)<$>readArray arr (i-m)|a<-as, let m=match!a, i-m>=0]
      case cands of
        [] -> return Nothing
        xs -> return $ Just $ maximumBy cmp xs

main :: IO ()
main = do
  n <- read . head . words <$> getLine
  as <- map head . words <$> getLine
  let result = runSTArray $ mm as n
  putStrLn . fst . fromJust $ result!n