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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

from fractions import gcd
from functools import reduce
def lcm(x, y):
    return (x // gcd(x, y))*y
def gcd_list(numbers):
    res = 1
    for n in numbers:
        res = lcm(n, res)
        if res>M:
            return -1
    return res


N, M = map(int, input().split())
a = list(map(int, input().split()))
aa = max(a)
A = gcd_list(a)
a = list(map(lambda x:x//2, a))
B = gcd_list(a)
a, b = M//A, M//B
if A == -1:
    a = 0
if B == -1:
    b = 0
if aa == A and aa<=M:
    print(b-a-1)
else:
    print(b-a)