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: Runtime Error)

import Control.Monad
import Control.Monad.ST
import Data.Array.ST
import Data.Array.Unboxed
import Data.STRef


dex :: Int
dex = 1000000007

main :: IO ()
main = do
  [n,m] <- map read . words <$> getLine
  as <- replicateM m readLn :: IO [Int]
  print $ solve (listArray (1,m) as) n m ! n

solve :: UArray Int Int -> Int -> Int -> UArray Int Int
solve xs n m = runSTUArray $ do
  dptbl <- newArray (1,n) 0
  ref   <- newSTRef 1
  forM_ [1..n] $ \i -> do
    p <- readSTRef ref
    if i == (xs!p)
      then writeArray dptbl i 0 >> writeSTRef ref (if p==m then p else p+1)
      else case i of
             1 -> writeArray dptbl 1 1
             2 -> liftM2 (+) (readArray dptbl 1) (return 1) >>= writeArray dptbl 2
             _ -> liftM2 (\x y -> (x+y)`mod`dex) (readArray dptbl (i-1)) (readArray dptbl (i-2)) >>= writeArray dptbl i

  return dptbl