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.

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.

Constraints

• $1 \leq N \leq 10^5$
• $0 \leq M \leq N-1$
• $1 \leq a_1 < a_2 < ... < a_M \leq N-1$

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.

见题面 Input 部分

见题面 Output 部分