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)

import Control.Applicative
import Control.Monad
import Control.Monad.ST
import Data.ByteString.Char8 (ByteString)
import qualified Data.ByteString.Char8 as B
import Data.List
import Data.Char (isSpace)
import Data.Vector.Unboxed.Mutable (IOVector, STVector)
import qualified Data.Vector.Unboxed.Mutable as VM
import Data.IntSet (IntSet)
import qualified Data.IntSet as IS

main :: IO ()
main = do
  [n, m] <- f
  solve n <$> (IS.fromList <$> replicateM m g) >>= print
  where
    f = readil B.readInt <$> B.getLine
    g = readi B.readInt <$> B.getLine

solve :: Int -> IntSet -> Int
solve n st = runST $ do
  sv <- VM.replicate (n + 1) 0 :: ST s (STVector s Int)
  VM.write sv 0 1
  if IS.member 1 st
    then VM.write sv 1 0
    else VM.write sv 1 1
  forM_ [2 .. n] $ \i -> do
    if IS.member i st
      then VM.write sv i 0
      else do
        x2 <- VM.read sv (i - 2)
        x1 <- VM.read sv (i - 1)
        VM.write sv i ((x1 + x2) `mod` md)
  VM.read sv n
  where
    md = 1000000007

readi :: Integral a =>  (ByteString -> Maybe (a, ByteString)) -> ByteString -> a
readi f s = let Just (n, _) = f s in n

readil :: Integral a =>  (ByteString -> Maybe (a, ByteString)) -> ByteString -> [a]
readil f = unfoldr $ \s -> do
  (n, s') <- f s
  return (n, B.dropWhile isSpace s')