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: Accepted)

MOD = 1000000007
def fib(n)
	#return n+1>>1 if n<4
	return ((0.5+Math.sqrt(5)*0.5)**n/Math.sqrt(5)).round % MOD if n<70
	nb = n.bit_length-6;a=((0.5+Math.sqrt(5)*0.5)**(n>>nb)/Math.sqrt(5)).round;b=(a+a*Math.sqrt(5)).round>>1
	(nb-1).downto(0){|m|a,b=a*(2*b-a)%MOD,(b*b+a*a)%MOD;a,b=b,a+b if (n>>m).odd?}
	return a
end

def mypow(a,m)
	return a**m%MOD if m<4;c,res=a,1;while(m>0);res=res*c%MOD if m.odd?;c,m=c*c%MOD,m>>1;end;return res
end

N, M = gets.split.map(&:to_i)
exit p(0) if M*2 > N
res = 1
$<.map(&:to_i).unshift(-1).push(N+1).each_cons(2).map{|x,y|y-x}.group_by(&:pred).each{|x,y|res=res*mypow(fib(x),y.size)%MOD}
p res