Contest Duration: ~ (local time) (100 minutes) Back to Home
C - Typical Stairs /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

N 段の階段があります。高橋君は現在、上り口(0 段目)にいます。 高橋君は一歩で 1 段か 2 段上ることができます。

ただし、a_1,a_2,a_3,....a_M 段目の床は壊れており、その段に足を踏み入れることは危険です。

制約

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

入力

N M
a_1
a_2
.
.
.
a_M


入力例 1

6 1
3


出力例 1

4


• 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

入力例 2

10 2
4
5


出力例 2

0


入力例 3

100 5
1
23
45
67
89


出力例 3

608200469


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.