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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
class c
{
    static void Main()
    {
        var nm = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        var ans = new long[nm[0] + 1];
        ans[0] = 1;
        for (int i = 0; i < nm[1]; i++)
        {
            ans[int.Parse(Console.ReadLine())] = -1;
        }
        for (int i = 1; i < ans.Length; i++)
        {
            if (ans[i] == -1) continue;
            if (i - 1 >= 0 && ans[i - 1] != -1)
            {
                ans[i] += ans[i - 1];
            }
            if (i - 2 >= 0 && ans[i - 2] != -1)
            {
                ans[i] += ans[i - 2];
            }
            ans[i] %= 1000000007;
        }
        Console.WriteLine(ans[ans.Length - 1]);
    }
}