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 qualified Data.ByteString.Char8 as BC
import Data.Maybe
import Control.Monad.ST
import Data.Array.Unboxed
import Data.Array.ST
import qualified Data.Set as Set

readIntLines :: IO [Int]
readIntLines = map (fst . fromJust . BC.readInt) . BC.lines <$> BC.getContents

solve :: Int -> Set.Set Int -> Int
solve n as = runSTUArray func ! n
  where
    func = do
      arr <- newArray (0, 10000) 0 :: ST s (STUArray s Int Int)
      mapM_ (iter arr) [0..10000]
      return arr
    iter a 0 = writeArray a 0 1
    iter a 1 = writeArray a 1 1
    iter a i = do
      v1 <- readArray a (i - 2)
      v2 <- readArray a (i - 1)
      let r1 = if Set.member (i - 2) as then 0 else v1
      let r2 = if Set.member (i - 1) as then 0 else v2
      writeArray a i ((r1 + r2) `mod` 1000000007)

main :: IO ()
main = do
  [n, m] <- map read . words <$> getLine
  as <- readIntLines
  print . solve n $ Set.fromList as