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 solve():
    from sys import stdin
    f_i = stdin
    
    N, M = map(int, f_i.readline().split())
    A = tuple(map(int, f_i.readline().split()))
    
    def fact2(num):
        cnt = 0
        while num % 2 == 0:
            num //= 2
            cnt += 1
    
    f = fact2(A[0])
    for a in A[1:]:
        if f != fact2(a):
            return 0
    
    from fractions import gcd
    def lcm(a, b):
        return a * b // int(gcd(a, b))
    
    import functools
    def mul_lcm(nums):
        return functools.reduce(lcm, nums)
    
    half_A = (a // 2 for a in A)
    g = mul_lcm(half_A)
    
    cnt = M // g
    q, r = divmod(cnt, 2)
    
    return q + r

print(solve())