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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;; D - Semi Common Multiple

(defun main ()
  (let* ((N (read))
         (M (read))
         (A (loop repeat N collect (read))))
    (princ (solve N M A))
    (fresh-line)))

(defun solve (N M A)
  (let* ((H (mapcar #'(lambda (x) (floor x 2)) A)) ; a_i / 2
         (lcm (loop for x in H
                    for l = x then (lcm l x) while (<= l M)
                    finally (return l)))) ; Hの最小公倍数
    (if (and (<= lcm M)
             (every #'(lambda (x) (oddp (floor lcm x))) H)) ; 全要素の奇数倍
        (ash (1+ (floor M lcm)) -1) ; M以下のlcmの奇数倍の個数
        0)))

(main)