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 Data.Foldable (maximumBy)
import Data.Maybe (catMaybes, fromJust)
import Data.Array (listArray, (!))

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

cmp :: StrL -> StrL -> Ordering
cmp (s1,l1) (s2,l2)
  | l1 > l2 = GT
  | l1 < l2 = LT
  | otherwise = cmp' s1 s2
  where
    cmp' [] [] = EQ
    cmp' (x:xs) (y:ys)
      | x > y = GT
      | x < y = LT
      | otherwise = cmp' xs ys

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

main :: IO ()
main = do
  n <- read . head . words <$> getLine
  as <- map head . words <$> getLine
  let result = listArray (0,n) $ map nth [0..] where
      nth 0 = Just ("",0)
      nth n =
        case catMaybes [(cons a)<$>result!(n-m)|a<-as, let m=match!a, n-m>=0] of
          [] -> Nothing
          xs -> Just $ maximumBy cmp xs
  putStrLn $ fst $ fromJust $ result!n