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)

import math
import sys
from fractions import gcd
m=10**9 + 7 
sys.setrecursionlimit(1000010)
(N, M) = list(map(int,input().split()))
B  = list(map(int,input().split()))

def lcmn(B):
    if len(B)<1 :
        return 1
    elif len(B) == 1:
        return B[0]
    
    x = B[0] * B[1] // gcd(B[0],B[1])
    if x > M*2:
        return -1 

    for i in range(2,len(B)):
        x  = lcmn([x,B[i]])
        if x > M*2:
            return -1 
    return x

        
x = lcmn(B)
if x == -1:
    print(0)
    exit(0)
if x > M * 2 :
    print(0)
    exit(0)
else:
    print(((M-x //2)//x+1))