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 Control.Monad
import Data.Char
import Data.List

main = do
    [n, m] <- fmap read <$> words <$> getLine
    a <- fmap read <$> words <$> getLine
    putStrLn $ solve n m a

solve :: Int -> Int -> [Int] -> String
solve n m a = doit n ""
  where
    doit i s | i >= (ms !! head pr) * 4 = doit (i - (ms !! head pr)) (s ++ show (head pr))
             | otherwise = max (maxnum ++ s) (s ++ maxnum)
      where
        maxnum = show $ head $ filter ok [99999, 99998 .. 1]
        ok num = all (\d -> elem d pr) ds && sum (map (ms !!) ds) == i
          where
            ds = map digitToInt $ show num
    ms = [100, 2, 5, 5, 4, 5, 6, 3, 7, 6]
    pr = filter (\i -> elem i a) [1, 7, 4, 5, 3, 2, 9, 6, 8]