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 (1.15.1) (judge verdict: Accepted)

fn main() {
    let (_n, mut m) = read_tuple::<i64>();
    let mut an: Vec<i64> = read_vec();

    let c = two_div_counter(an[0]);
    for a in an.iter_mut() {
        let ac = two_div_counter(*a);
        if c != ac {
            println!("0");
            std::process::exit(0);
        }
        *a >>= c;
    }
    m >>= c-1;
    let t = lcm(&an);
    m /= t;

    println!("{:?}", (m+1)/2);
}

fn two_div_counter(n: i64) -> i64 {
    let mut a = n;
    let mut count = 0;
    while a % 2 == 0 {
        count += 1;
        a /= 2;
    }
    count
}

pub fn gcd(a: i64, b: i64) -> i64 {
    let (mut a, mut b) = (a, b);
    while b != 0 {
        let tmp = a - (a / b) * b;
        a = b;
        b = tmp;
    }
    a
}


pub fn lcm(iterable: &Vec<i64>) -> i64 {
    let mut a = iterable[0];
    for b in iterable.iter() {
        a = a / gcd(a, *b) * b;
    }
    a
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}
fn read_tuple<T: std::str::FromStr + Copy>() -> (T, T) {
    let temp = read_vec();
    (temp[0], temp[1])
}