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 PyPy2 (5.6.0) (judge verdict: Wrong Answer)

import collections
n,m = map(int, raw_input().split(' '))
elems = map(int, raw_input().split(' '))

def gcd(a,b):
	return gcd(b,a%b) if b else a

def lcm(a,b):
	return a * b / gcd(a,b)

for i in range(len(elems)):
	elems[i] /= 2

glcm = reduce(lcm, elems)

count = m / glcm
count-= count/2
print count

"""
x = ak * (p + 0.5)

x = ak/2 2p + ak/2
x = ak/2 * (2p+1)

x is a multiple of ak/2, with an odd pp (2p + 1)
for all k
x is a muliple of lcm([ak/2 for k in range(n)])

"""