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: Wrong Answer)

a,b = gets.chomp.split(" ").map(&:to_i)
numbers = gets.split(" ").map(&:to_i)
i = 0
array = []
list = [0,0]
while list.any? {|w| w <= b }
  	list = []
    array << numbers.map{ |x| x * (0.5+i) }
  	list  << numbers.map{ |x| x * (0.5+i) }
  	array = array.flatten
  	list = list.flatten
  	i += 1
end
array = array.sort
deplication = []
m = 0
j = 0
array.each do |n|
  if n == m
    j += 1
  else
    deplication << j
    j = 0
  end
  m = n
end
p deplication.count(a-1)