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(x, y)
  if y == 0
    return x
  else
    gcd(y, x % y)
  end
end

def main
  n, m = gets.chomp.split.map(&:to_i)
  a = gets.chomp.split.map(&:to_i)
  
  #aを2で割る
  a = a.map {|v| v / 2}

  #aを２で割り切れるだけ割る
  isSame = true
  while a[0] % 2 == 0 do
    n.times do |i|
      if a[i] % 2 == 0
        a[i] /= 2
      else
        isSame = false
      end 
    end
    m /= 2
  end

  return 0 if isSame == false
  a.each do |v|
    return 0 if v % 2 == 0
  end

  #aの最小公倍数を求める
  lcm = 1
  n.times do |i|
    g = gcd(lcm, a[i])
    lcm = (lcm / g) * a[i] 
    return 0 if lcm > m
  end

  #m以下の中でlcmの奇数倍の総和を求める
  return (m / lcm + 1) / 2
end

puts main