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: Wrong Answer)

use std::cmp::{max, min};

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()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn gcd(a: usize, b: usize) -> usize {
    match ((a, b), (a & 1, b & 1)) {
        ((x, y), _) if x == y => y,
        ((0, x), _) | ((x, 0), _) => x,
        ((x, y), (0, 1)) | ((y, x), (1, 0)) => gcd(x >> 1, y),
        ((x, y), (0, 0)) => gcd(x >> 1, y >> 1) << 1,
        ((x, y), (1, 1)) => {
            let (x, y) = (min(x, y), max(x, y));
            gcd((y - x) >> 1, x)
        }
        _ => unreachable!(),
    }
}

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

fn main() {
    let v: Vec<usize> = read_vec();
    let _n = v[0];
    let m = v[1];
    let a_vec: Vec<usize> = read_vec();

    let b_vec: Vec<usize> = a_vec.iter().map(|a| a / 2).collect();

    let mut d = b_vec[0];
    for b in b_vec {
        d = lcm(d, b);
        if d > m {
            println!("0");
            return;
        }
    }

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