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 ScopedTypeVariables #-}
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.ByteString.Char8 as BS
import Control.Monad
import Control.Monad.ST
import Control.Applicative
import Data.Maybe

m :: Int
m = 10^9+7

solve :: VUM.IOVector Bool -> VUM.IOVector Int -> Int -> IO Int
solve oks dp n = do  
  forM_ [0..n-1] $ \i ->
    forM_ [i+1..min n (i+2)] $ \j -> do
      judge <- VUM.read oks j
      when judge $ do
        now <- VUM.read dp i
        next <- VUM.read dp j
        VUM.write dp j ((now+next) `rem` m)
  VUM.read dp n

main = do
  [n, m] <- map read . words <$> getLine :: IO [Int]
  (oks :: VUM.IOVector Bool) <- VUM.replicate (n+1) True
  forM_ [1..m] $ \_ -> do
    x <- BS.getLine
    let Just (i,_) = BS.readInt x
    VUM.write oks i False
  
  (dp :: VUM.IOVector Int) <- VUM.replicate (n+1) 0
  VUM.write dp 0 1
  solve oks dp n >>= print