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).

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).

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.

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

见题面 Input 部分

见题面 Output 部分