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: Wrong Answer)

from fractions import gcd
#from math import gcd
N,M = map(int,input().split())
A = list(map(int,input().split()))
lcm = A[0]
ki = 0; gu = 0
k4 = 0; g4 = 0
if (A[0]//2)%2 == 1:
    ki = 1
else:
    gu = 1
    if A[0]%8 == 4:
        k4 = 1
    else:
        g4 = 1

for i in range(1,N):
    if (A[i]//2)%2 == 1:
        ki = 1
    else:
        gu = 1
        if A[i]%8 == 4:
            k4 = 1
        else:
            g4 = 1
    if ki*gu == 1:
        print(0)
        exit()
    if k4*g4 == 1:
        print(0)
        exit()
    lcm = (lcm*A[i]) // gcd(lcm,A[i])
    if lcm > 2*M:
        print(0)
        exit()

M -= lcm//2
ans = (M//lcm)+1
print(ans)