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)

from fractions import gcd

N,M=map(int,input().split())
#List=list(map(lambda x:int(x)/2,input().split()))
List=list(map(int,input().split()))


LCM=1
cut2count=0
a=List[0]/2
while a%2==0:
    a/=2
    cut2count+=1

for i in List:
    i/=2
    LCM*=i/gcd(LCM,i)
        
    cut2countb=0
    b=i
    while b%2==0:
        b/=2
        cut2countb+=1
    if cut2count!=cut2countb:
        print(0)
        exit()


#for i in List:
 #   if LCM/i%2==0:
  #      print(0)
   #     exit()

print(int(M//(LCM*2)+M%(LCM*2)//LCM))