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)

n,m = map(int,input().split())

a = [0]*n
a = [int(s) for s in input().split()]

a_half = [s//2 for s in a]
#print(a)

def check(x):
    while (all(c%2 == 0 for c in x)):
        x = [s//2 for s in x]
        if any(c%2 == 1 for c in x) and any(c%2 == 0 for c in x):
            return 0
        
    
    return 1

def gcd(x,y):
    #print(x,y)
    if(x%y == 0):
        #print(y)
        return y
    else:
        return gcd(y,x%y)


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

if(check(a)== 1):
    x = a_half[0]
    for i in range(1,n):
        y = a_half[i]
        x = lcm(x,y)
    if(x > m):
        print(0)
    else:
        res = int((m//x+1)//2)
        print(res)
else:
    print(0)