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: Runtime Error)

import math

# define
a = [0] * int(1e5 + 100)
# functions
# main

n, m = (int(s) for s in input().split())

inp = input().split()
for i in range(1, n + 1) :
    a[i] = int(inp[i - 1])

flag = False
lcm = a[1]

for i in range(2, n + 1) :
    gcd = math.gcd(lcm, a[i])
    #lcm = int(lcm * a[i] / gcd)
    if(lcm > m):
        flag = True
        break

for i in range (1, n + 1):
    if lcm / a[i] % 2 == 0 : flag = True

if flag or lcm > m : print(0)
else : print(int( (m - int(lcm / 2)) / lcm ) + 1)