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)

# coding: utf-8
import fractions
from functools import reduce
from math import ceil, floor

def gcd_list(numbers):
    return reduce(fractions.gcd, numbers)

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

def lcm_list(numbers):
    return reduce(lcm, numbers)

N, M = map(int, input().split())
A = list(map(int, input().split()))
for i in range(N):
    A[i] //= 2
G = gcd_list(A)
L = lcm_list(A)
# l = L // G
# print(G, L)
# ans = (M // l) // 2
# print(ans if ans == 0 else ans + 1)
print(ceil(M / L)//2)