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 solve(lscm,m)
    # least semi common multiple
    return ( m / lscm + 1 ) / 2 

end

n, m = gets.split.map(&:to_i)
a = gets.split.map(&:to_i)

b = a.map do |k|
    
    res = 0
    while k.even?
        k /= 2
        res += 1
    end
    res
end
# p a
# p b
ans = 0
if b.uniq.size == 1
    lscm = a.map{|k| k/2}.inject(:lcm)
    # p lscm
    # p a
    # p b
    ans = solve(lscm, m)
end

puts ans



# a/2 * (2p+1)