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 Ruby (2.3.3) (judge verdict: Runtime Error)

n, m = gets.split.map(&:to_i)
a = Array.new(m){gets.to_i}
a << n + 1
t = Array.new(m + 1){0}
c = 0
(0...m).each{|i|
	if a[i + 1] - a[i] == 1
		puts 0
		return
	end
}
a.each_index{|i|
	w = a[i] - c - 1
	0.upto(w / 2){|x|
		y = w - x * 2
		if x > y
			tmp = x
			x = y
			y = tmp
		end
		if x == 0
			t[i] += 1
		else
			t[i] += (1..x).inject(((y + 1)..(x + y)).inject(:*), :/)
		end
	}
	c = a[i] + 1
}
puts t.inject(:*) % 1000000007