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: Runtime Error)

import fractions
from functools import reduce
import math
def lcm_base(x, y):
    return int((x * y) // fractions.gcd(x, y))
def lcm_list(numbers):
    return int(reduce(lcm_base, numbers, 1))

N,M = map(int,input().split())
List=list(map(int,input().split()))
aa = int(lcm_list(List)/2)
cnt = 0
a=List[0]
while a%2 == 0:
  cnt+=1
  a = int(a/2)
out = 0
if cnt == 0:
  out = 1
  cnt = 1
for i in range(len(List)):
  if List[i] % (2**cnt) == 1:
    out = 1
  elif List[i] % (2**(cnt+1)) == 0:
    out = 1

if out == 1:
  print(0)
else:
  print(int(math.ceil((M / aa)) // 2))