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 (3.8.2) (judge verdict: Accepted)

import math

def n_2(n):
  c=0
  while n%2==0:
    c+=1
    n>>=1
  return (n,c)

N,M=map(int,input().split())
A=list(map(int,input().split()))
A[0],a=n_2(A[0])
p=False
for i in range(1,N):
  A[i],b=n_2(A[i])
  if a!=b:
    p=True
    break
if p:
  print(0)
  exit()
n=1
for _ in range(a-1):
  n*=2
l=n
for a in A:
  l=l*a//math.gcd(l,a)
ans=M//l-M//(2*l)
print(ans)