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 (2.7.1) (judge verdict: Time Limit Exceeded)

def conv(a,b)
  if b > a/2
    b = a - b
  end
  ans = 1
  div = 1
  b.times do |i|
    ans *= a - i
    ans %= MOD
    div *= (i+1)
    div %= MOD
  end
  ans = ans * pow(div, MOD-2)
  ans % MOD
end

def pow(x,n)
  if n == 0
    1
  elsif n % 2 == 0
    pow(x*x%MOD, n/2) % MOD
  else
    x * pow(x, n-1) % MOD
  end
end

MOD = 10**9+7
n,m = gets.chomp.split(" ").map(&:to_i)
a = []
m.times do |i|
  a[i] = gets.to_i
end
count = 1
indi = 0
(m+1).times do |i|
  count_mid = 0
  if i == m
    step = n - indi
  else
    step = a[i]-1 - indi
  end
  step2 = step/2
  step1 = step%2
  while step2 > 0
    count_mid += conv(step2+step1,step1)
    count_mid %= MOD
    step2 -= 1
    step1 += 2
  end
  count_mid += 1
  count = count * count_mid
  count %= MOD
  if i != m
    indi = a[i]+1
  end
  if i > 0 && i != m
    if a[i]-1 == a[i-1]
      puts 0
      exit
    end
  end
end
puts count