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)

N, M = gets.chomp.split(" ").map(&:to_i)
A = gets.chomp.split(" ").map(&:to_i).uniq

require "prime"

pr = {}
A.each do |a|
  if a % 2 == 1
    puts 0
    exit
  end
  (a/2).prime_division.each do |e, n|
    # 素因数の2のべき乗項は全てのaで共通である必要がある
    if e == 2 && pr[2] && pr[2] != n
      puts 0
      exit
    end
    pr[e] ||= n
    pr[e] = n if n > pr[e]
  end
end

mul = 1
pr.each do |e, n|
  mul *= e**n
end

m = M / mul
if m % 2 == 0
  puts m / 2
else
  puts m / 2 + 1
end