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)

use std::io::Write;

#[allow(unused)]
macro_rules! debug {
    ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
    ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}

fn main() {
    let (n, m): (u64, u64) = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let s = s.trim_right().to_owned();
        let mut ws = s.split_whitespace();
        let a = ws.next().unwrap().parse().unwrap();
        let b = ws.next().unwrap().parse().unwrap();
        (a, b)
    };

    let a: Vec<u64> = {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        let s = s.trim_right().to_owned();
        s.split_whitespace().map(|x| x.parse().unwrap()).collect()
    };

    let b: Vec<u64> = a.iter().map(|x| x / 2).collect();
    // let lcm_all = b.iter().fold(1, |acc, x| lcm(acc, *x));
    let mut lcm_all = 1;
    for &x in &b {
        lcm_all = lcm(lcm_all, x);
        if lcm_all > 10u64.pow(9) {
            // debugln!("overflow");
            println!("0");
            return;
        }
    }

    for &x in &b {
        if (lcm_all / x) % 2 == 0 {
            println!("0");
            return;
        }
    }

    let l = m / lcm_all;
    println!("{}", (l + 1) / 2);
}

fn gcd(a: u64, b: u64) -> u64 {
    let c = a % b;
    if c == 0 {
        b
    } else {
        gcd(b, c)
    }
}

fn lcm(a: u64, b: u64) -> u64 {
    (a * b) / gcd(a, b)
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn lcm_test() {
        assert_eq!(6, lcm(2, 3));
        assert_eq!(12, lcm(4, 6));
        assert_eq!(30, lcm(6, 10));
        assert_eq!(2, lcm(2, 2));
        assert_eq!(6, lcm(1, 6));
    }
}