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 Rust (1.42.0) (judge verdict: Accepted)

fn input_pair<T: std::str::FromStr + Copy> () -> (T, T) {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let arr: Vec<_> = s.trim().split_whitespace().flat_map(str::parse).collect();
    (arr[0], arr[1])
}

fn input_arr<T: std::str::FromStr> () -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().flat_map(str::parse).collect()
}

fn gcd(a: usize, b: usize) -> usize {
    if a == 0 {
        b
    } else {
        gcd(b % a, a)
    }
}

fn main() {
    let (n, m) = input_pair::<usize>();
    let arr: Vec<usize> = input_arr();

    let x = arr.iter().fold(1, |a, &b| a * b / gcd(a, b));
    if arr.iter().all(|a| (x / a) % 2 == 1) {
        println!("{}", 2 * m / x - m / x);
    } else {
        println!("0");
    }
}