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)

lines = readlines.map{|line| line.split(' ').map(&:to_i)}
b=lines[1].map{|e|e.to_i/2}.inject(:lcm)
a=[]
for i in 0..lines[0][0]-1
  a[i]=0
  while lines[1][i]%2==0 do
    lines[1][i]=lines[1][i]/2
    a[i]=a[i]+1
  end
end
a.delete(a[0])
if a==[] then
  if lines[0][1]>=b then
    if lines[0][1]/b%2==0 then
      puts lines[0][1]/b/2
    else
      puts lines[0][1]/b/2+1
    end
  else
    puts 0
  end
else
  puts 0
end