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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

def lcm(x, y):
    return x * y // gcd(x, y)
def gcd(x, y):
    if y == 0:
        return x
    return gcd(y, x % y)

def twos(x):
    m = 16
    ret = 0
    while True:
        if x % (1 << m) == 0:
            x = x >> m
            ret += m
        if m == 0:
            break
        m = m >> 1
    return ret

n, m = map(int, input().split())
a = list(map(int, input().split()))
b = [x // 2 for x in a]

# check
p = twos(a[0])
for x in a:
    if twos(x) != p:
        print(0)
        exit()

l = lcm(b[0], b[0])
for x in b:
    l = lcm(l, x)

print((m // l + 1)//2)