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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

#D
import math
N,M = map(int,input().split())
A = list(map(int,input().split()))
B = []
for i in range(N):
    if A[i] not in B:
        B.append(A[i])
    else:
        N-=1

def GCD(x,y):
    x,y = max(x,y),min(x,y)
    if y == 0:
        return x
    else:
        return GCD(y,x%y)
    
g = B[0]
for i in range(N-1):
    g = GCD(B[i+1],g)
    
bai = g
for i in range(N):
    bai*=B[i]//g
    
han = bai//2
print(math.ceil((M//han)/2))