Reference: AtCoder ABC150 D — Semi Common Multiple

You are given a sequence ~A~ of ~N~ positive even integers:

~a_1, a_2, \ldots, a_N~

and an integer ~M~.

A positive integer ~X~ is called a semi-common multiple of ~A~ when, for every ~k~ from ~1~ to ~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~ between ~1~ and ~M~, inclusive.

Input

• The first line contains two integers ~N~ and ~M~.
• The second line contains ~N~ integers: ~a_1, a_2, \ldots, a_N~.

Output

• Print the number of semi-common multiples between ~1~ and ~M~, inclusive.

Constraints

• ~1 \le N \le 10^5~
• ~1 \le M \le 10^9~
• ~2 \le a_i \le 10^9~
• Every ~a_i~ is even, and all input values are integers.

Example 1

Input:

2 50
6 10

Output:

2