C - Typical Stairs

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 $1\ 000\ 000\ 007$.

6 1
3

4

There are four ways to climb up the stairs, as follows:

• $0 \to 1 \to 2 \to 4 \to 5 \to 6$
• $0 \to 1 \to 2 \to 4 \to 6$
• $0 \to 2 \to 4 \to 5 \to 6$
• $0 \to 2 \to 4 \to 6$

10 2
4
5

0

There may be no way to climb up the stairs without setting foot on the broken steps.

100 5
1
23
45
67
89

608200469

Be sure to print the count modulo $1\ 000\ 000\ 007$.