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: Accepted)

import fractions, sys
input = sys.stdin.buffer.readline


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


def calc(n, m):
    for i in range(cycle//m+1):
        X = m * (i + 0.5)
        if X > M:
            print(0)
            exit()
            return
        flag = True
        for x in n:
            if (X - x // 2) % x != 0:
                flag = False
                break
        if flag:
            return int(X)
    print(0)
    exit()
    return


N, M = map(int, input().split())
A = list(map(int, input().split()))
cycle = 1
ma = 0
for a in A:
    cycle = lcm(cycle, a)
    ma = max(ma, a)
start = calc(A, ma)

print((M - start) // cycle + 1)