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