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)

from functools import reduce
from fractions import gcd
#from math import gcd

def lcm(a, b):
    return  a//gcd(a, b) * b

n,m=map(int,input().split())
a=list(map(int,input().split()))

b=[0]*n
for i in range(n):
    b[i]=a[i]//2

lcma=reduce(lcm,b)   

yn=""
for i in range(n):
    if (lcma//b[i])%2==0:
        yn="no"
        break
    
if yn=="no":
    print(0)
else:    
    ans=m//lcma
    ans2=ans//2
    if (ans2*2+1)*lcma<=m:
        ans2+=1
    print(ans2)