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 qualified Data.List
import qualified Data.Char
import Debug.Trace
import qualified Data.Sequence as Seq

main ::IO()
main = do
  [n,m] <- map read . words <$> getLine :: IO [Int]
  as <- replicateM m $ read <$> getLine :: IO [Int]
  putStrLn $ show $ solve n as

solve :: Int -> [Int] -> Int
solve n as =
  -- traceShow (take n cands) $
  ans
  where
    isBrokenL = brokenListToBool as [0..]
    cands =  dp f $ tail isBrokenL
    ans = cands !! (n+1)

f isBroken prevCombo prevPrevCombo =
  -- traceShow cand $
  cand
  where
    cand =
      if isBroken then 0
      else (prevCombo + prevPrevCombo)  `mod` 1000000007

-- brokenListToBool [] [] = []
brokenListToBool [] _ = repeat False -- False : brokenListToBool [] bs' 
brokenListToBool as@(a:as') (b:bs') 
  | a==b =  True : brokenListToBool as' bs'
  | otherwise = False : brokenListToBool as bs'
  

-- functions --

dp f l =
  combos
  where
    combos = 0 : 1 : zipWith3 f l combos (tail combos)