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: Accepted)

N, M = map(int, input().split())
l = sorted(list(set(map(int, input().split()))))

df = l[0]
#print("df", df)

s = len(bin(df)) - 2
#print("s", s)

count = 0
for i in range(s):
    if df % 2:
        break
    df //= 2
    count += 1
    
#print("count", count)

l = tuple(map(lambda x:x // (2**count), l))
#print("l", l)

for i in l:
    if i % 2 == 0:
        print(0)
        exit()

def gcd(a, k):
    if k:
        return gcd(k, a % k)
    return a

ans = l[0]
for i in l:
    ans = ans * i // gcd(ans, i)

print(-(-(M // (ans * 2**(count - 1))) // 2))