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: Time Limit Exceeded)

-- vim: set fdm=marker : -- {{{
{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE BangPatterns #-}
import Control.Monad
import Control.Monad.Fix (fix)
import Data.Maybe
import Data.Array.Unboxed (Array, Ix, array, (!), range)
import qualified Data.ByteString.Char8 as BS

tuplify2 (x:y:_) = (x,y)
tuplify2 _ = undefined

--Input functions with ByteString
readInt :: Num a => BS.ByteString -> a
readInt = fromIntegral . fst . fromJust . BS.readInteger
readIntTuple :: Num a => BS.ByteString -> (a, a)
readIntTuple = tuplify2 . map readInt . BS.words
readIntList :: Num a => BS.ByteString -> [a]
readIntList = map readInt . BS.words

getInt :: Num a => IO a
getInt = readInt <$> BS.getLine
getIntList :: Num a => IO [a]
getIntList = readIntList <$> BS.getLine
getIntN n = map readInt <$> replicateM (fromIntegral n) BS.getLine
getIntNList n = map readIntList <$> replicateM (fromIntegral n) BS.getLine
getIntMatrix = map readIntList . BS.lines <$> BS.getContents
getIntTuple = readIntTuple <$> BS.getLine
getIntNTuples n = map readIntTuple <$> replicateM (fromIntegral n) BS.getLine
getIntTuples = map readIntTuple . BS.lines <$> BS.getContents
-- }}}

type Index = Int
type Value = Integer
type Data  = Array Int Int

main = do
    [n,m] <- getIntList :: IO [Int]
    as <- getIntN m :: IO [Int]
    print $ slvMemo n (genArray m as) 0 `mod` 1000000007

genArray :: Int -> [Int] -> Data
genArray n xs = array (0, n-1) [x | x <- zip [0..n] xs]

memo :: (Index -> a) -> (Index -> a)
memo !f = (map f [0..] !!)

slvMemo :: Int -> Data -> Index -> Value
slvMemo !n !d = fix (memo . slv n d)

slv :: Int -> Data -> (Index -> Value) -> Index -> Value
slv !n !d !f !i
  | i `elem` d = 0
  | i  > n = 0
  | i == n = 1
  | i == (n-1) = 1
  | otherwise = f (i+1) + f (i+2)