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 v = read_vec::<u64>();
    let n = v[0];
    let m = v[1];
    let a = read_vec::<u64>();

    let a_half = a.into_iter().map(|ai| ai / 2).collect::<Vec<_>>();
    let mut a_gcd = a_half[0];
    for i in 1..n as usize {
        a_gcd = gcd(a_gcd, a_half[i]);
    }

    let a2 = a_half.into_iter().map(|ai| ai / a_gcd).collect::<Vec<_>>();
    let mut a_lcm = 1;
    for ai in a2 {
        if ai % 2 == 0 {
            println!("0");
            return;
        } else {
            a_lcm = lcm(a_lcm, ai);
        }
    }
    let aa = a_gcd * a_lcm;
    let ans = if (m / aa) % 2 == 0 {
        m / (aa * 2)
    } else {
        m / (aa * 2) + 1
    };
    println!("{}", ans);
}

fn gcd(x: u64, y: u64) -> u64 {
    if x == 0 {
        y
    } else {
        gcd(y % x, x)
    }
}

fn lcm(x: u64, y: u64) -> u64 {
    x * y / gcd(x, y)
}

#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}
#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}
#[allow(dead_code)]
fn yn(result: bool) {
    if result {
        println!("Yes");
    } else {
        println!("No");
    }
}