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: Wrong Answer)


def gcd(a, b):
    r = 0
    while True:
        if b > a:
            a, b = b, a
        r = a % b
        if r == 0:
            return b
        a = b
        b = r
def lcm(a, b):
    g = gcd(a, b)
    return (a // g) * b
res = 0
def func():
    global res
    N, M = [int(i) for i in input().split()]
    A = [int(i) // 2 for i in input().split()]

    for i in A:
        if i % 2 == 0:
            return
    ok = []
    
    n = A[0]
    for i in range(N - 1):
        n = lcm(n, A[i + 1])
    if M // 2 < n:
        res = 1
    else:
        res = M // n // 2
        if M >= 2 * n:
            res += 1
func()
print(res)