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 (2.4.0) (judge verdict: Wrong Answer)

import sys

N, M = map(int, input().split())
A = list(set([i for i in map(int, sys.stdin.readline().split())]))

if len(A) > 1:
  a, b = A[0], A[1]
  while b > 0:
    a, b = b, a%b
  
  if len(A) > 2:
    for b in A[2:]:
      while b > 0:
        a, b = b, a%b
        
else:
  a = A[0]
    
prod = 1
for _a in A:
  prod *= _a
  
CM = prod // a
SCM = CM // 2

if SCM > M:
  print(0)
else:
  print(1 + (M - SCM) // CM)