Problem:
Score : 400 points

Problem Statement

Given are a sequence A= {a_1,a_2,......a_N} of N positive even numbers, and an integer M.

Let a semi-common multiple of A be a positive integer X that satisfies the following condition for every k (1 \leq k \leq N):

There exists a non-negative integer p such that X= a_k \times (p+0.5).

Find the number of semi-common multiples of A among the integers between 1 and M (inclusive).

Constraints

1 \leq N \leq 10^5

1 \leq M \leq 10^9

2 \leq a_i \leq 10^9

a_i is an even number.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
a_1 a_2 ... a_N

Output

Print the number of semi-common multiples of A among the integers between 1 and M (inclusive).

Sample Input 1

2 50
6 10

Sample Output 1

2

15 = 6 \times 2.5

15 = 10 \times 1.5

45 = 6 \times 7.5

45 = 10 \times 4.5

Thus, 15 and 45 are semi-common multiples of A. There are no other semi-common multiples of A between 1 and 50, so the answer is 2.

Sample Input 2

3 100
14 22 40

Sample Output 2

0

The answer can be 0.

Sample Input 3

5 1000000000
6 6 2 6 2

Sample Output 3

166666667

Solution in Ruby (2.3.3) (judge verdict: Accepted)

n,m = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)

if a.index{|v| v.odd?}
  p 0
  exit
end

mul = 1
while a.index{|v| v.odd?}.nil?
  a.map!{|v| v/2}
  mul *= 2
end

if a.all?{|v| v.odd?}
  minX = mul / 2
  a.each do |v|
    minX = minX.lcm(v)
    if minX > m
      p 0 
      exit
    end
  end
  ans = (m / minX + 1) / 2
  p ans
else
  p 0
end