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)

def gcd(a, b)
  return a if b == 0
  gcd(b, a%b)
end

def lcm(a, b)
  a, b = b, a if b > a
  a * b / gcd(a,b)
end

def f(n)
  cnt = 0
  while n%2 == 0
    n /= 2
    cnt += 1
  end
  cnt
end

N, m = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)
a = a.map!{|n| n/2}

flag = true
ni = f(a[0])
N.times do |i|
  if ni != f(a[i])
    flag = false
    break
  end
end

if flag
  a.map!{|n| n/(2**ni)}
  m /= 2 ** ni
  l = 1
  N.times do |i|
    l = lcm(l, a[i])
  end
  puts ((m/l) + 1)/2
else
  puts 0
end