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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import copy
N, M = map(int, input().split())
a = list(map(int, set(input().split())))
N = len(a)

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

def gcd(a, b):
  if a < b:
    a, b = b, a
  while (b > 0):
    temp = a%b
    a = b
    b = temp
  return a

def multi_lcm(arr):
  temp = arr.pop(0)
  for i in arr:
    temp = lcm(i, temp)
  return temp

if N == 1:
  if a[0] > M:
    print("0")
    exit()
  else:
    print(1 + int((M - (a[0] / 2)) // a[0] ))
    exit()

temp = 0
temp2 = a[0]
temp3 = 0
while temp2 % 2 == 0:
  temp2 = temp2 / 2
  temp += 1
for i in a:
  temp2 = i
  temp3 = 0
  while temp2 % 2 == 0:
    temp2 = temp2 / 2
    temp3 += 1
  if temp != temp3:
    print("0")
    exit()
    
  
a_lcm = multi_lcm([i/2 for i in a])
inc = multi_lcm(copy.copy(a))
inc = 2 * a_lcm

if a_lcm > M:
  print(0)
  exit()
print(1 + int((M - a_lcm) // inc))