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: Accepted)

import fractions
import numpy as np

N, M = map(int,input().split())
A = list(map(int,input().split()))

def lcm(x, y):
    return (x * y) // fractions.gcd(x, y)

bef = 1
LCM = 1
ans = []
for i,a in enumerate(A):
    LCM = lcm(LCM,a)
    if bef !=1:
        c, d = bef, a//2
        while c % 2 == 0 and d % 2 == 0:
            c //= 2
            d //= 2
        if c%2 != d%2:
            print(0)
            exit()
    
    b = a//2
    bef = lcm(bef,b)
    ans.append(bef)

print((M-bef)//LCM+1)