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 Python (3.4.3) (judge verdict: Wrong Answer)

#import sys
#input = sys.stdin.buffer.readline

def main():
    #print(arg)
    #input = arg.split("\n")
    N,M = list(map(int, input().split(" ")))
    #print(input)
    #return
    A = [int(input()) for i in range(M)]
    #print(N)
    #print(M)
    print(A)

    #return

    if len(A) > 1:
        for i in range(1,M):
            if A[i] - A[i-1] == 1:
                print(0)
                return


    dp = [0] * (N-M+1)
    dp[0] = 1

    for i in range(1,N-M+1):
        dp1 = dp[i-1]%1000000007
        dp2 = 0
        if i >= 2:
            dp2 = (dp[i-2]*2)%1000000007
        
        print("i={0}: dp1={1}, dp2={2}".format(i, dp1, dp2))
        dp[i] = max(dp1, dp2)
        
    print(dp[N-M])

#main("6 1\n3")
main()