typicalstairs
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 a1-th, a2-th, a3-th, \ldots, aM-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 ≤ N ≤ 105
- 0 ≤ M ≤ N-1
- 1 ≤ a1 < a2 < ... < aM ≤ N-1
Input
Input is given from Standard Input in the following format:
N M
a1
a2
.
.
.
aM
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.