Problem:
Score : 300 points

Problem Statement

There is a staircase with N steps. Takahashi is now standing at the foot of the stairs, that is, on the 0-th step.
He can climb up one or two steps at a time.

However, the treads of the a_1-th, a_2-th, a_3-th, \ldots, a_M-th steps are broken, so it is dangerous to set foot on those steps.

How many are there to climb up to the top step, that is, the N-th step, without setting foot on the broken steps?
Find the count modulo 1\ 000\ 000\ 007.

Constraints

1 \leq N \leq 10^5

0 \leq M \leq N-1

1 \leq a_1 < a_2 < ... < a_M \leq N-1

Input

Input is given from Standard Input in the following format:

N M
a_1
a_2
.
.
.
a_M

Output

Print the number of ways to climb up the stairs under the condition, modulo 1\ 000\ 000\ 007.

Sample Input 1

6 1
3

Sample Output 1

4

There are four ways to climb up the stairs, as follows:

0 \to 1 \to 2 \to 4 \to 5 \to 6

0 \to 1 \to 2 \to 4 \to 6

0 \to 2 \to 4 \to 5 \to 6

0 \to 2 \to 4 \to 6

Sample Input 2

10 2
4
5

Sample Output 2

0

There may be no way to climb up the stairs without setting foot on the broken steps.

Sample Input 3

100 5
1
23
45
67
89

Sample Output 3

608200469

Be sure to print the count modulo 1\ 000\ 000\ 007.

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

{-# LANGUAGE RankNTypes #-}
    
import Control.Monad.State
import Control.Monad.ST
import Data.Array.ST
import Control.Arrow
import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Set as S

main :: IO ()
main = readLine >>= main'
    where
        main' [n, m] = replicateM m (head <$> readLine) >>= print . solve n

solve :: Int -> [Int] -> Int
solve n as = runST (initialize >>= stAction)
    where
        initialize :: ST s (Table s Int a)
        initialize = newArray (0, 10 ^ 6) Nothing

        s = S.fromList as
        
        stAction = evalMemo calc 0

        calc f i
            | i > n = return 0
            | i == n = return 1 
            | S.member i s = return 0
            | otherwise = add <$> f (i + 1) <*> f (i + 2)

readLine :: IO [Int]
readLine = unfoldr (fmap (second (maybe B.empty snd . B.uncons)) . B.readInt) <$> B.getLine

readContents :: Int -> IO [[Int]]
readContents = flip replicateM readLine

infixl 6 `add`
infixl 7 `mul`

add :: Int -> Int -> Int
add x y = val $ x + y

mul :: Int -> Int -> Int
mul x y = val $ x * y

inv :: Int -> Int
inv x = pow x $ modVal - 2

pow :: Int -> Int -> Int
pow b e
    | e == 0 = 1
    | odd e = mul b . pow b $ e - 1
    | otherwise = mul v v
    where
        v = pow b $ e `div` 2

val :: Int -> Int
val = (`mod` modVal)

modVal :: Int
modVal = 10 ^ 9 + 7

primes :: [Int]
primes = build [2..]
    where
        build (x : xs) = x : build (filter (\n -> n `mod` x /= 0) xs)
        
isPrime :: Int -> Bool
isPrime n = check primes
    where
        check (x : xs)
            | x == n = True
            | x > n = False
            | otherwise = check xs

type Table s a b = STArray s a (Maybe b)
type Memo s a b = a -> StateT (Table s a b) (ST s) b

evalMemo :: (Ix a) => (forall s. Memo s a b -> Memo s a b) -> a -> Table s a b -> ST s b
evalMemo f k = evalStateT (memoizeFix f k)

runMemo :: (Ix a) => (forall s. Memo s a b -> Memo s a b) -> a -> Table s a b -> ST s (b, Table s a b)
runMemo f k = runStateT (memoizeFix f k)

memoizeFix :: (Ix a) => (forall s. Memo s a b -> Memo s a b) -> forall s. Memo s a b
memoizeFix f k = get >>= (\arr -> lift (readArray arr k) >>= maybe (f (memoizeFix f) k >>= ((<$) <*> (lift . writeArray arr k . Just))) return)