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)

// -*- coding:utf-8-unix -*-

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: usize,
        m: usize,
        a: [usize; n],
    }
    let num2 = num_of_factor2(a[0]);
    for i in 2..=n {
        if num2 != num_of_factor2(a[i - 1]) {
            println!("0");
            return;
        }
    }
    let mut alcm = 1;
    for &ai in &a {
        alcm = lcm(alcm, ai / 2);
    }
    let mut tmp1 = m / alcm;
    if tmp1 % 2 != 0 {
        tmp1 += 1;
    }
    println!("{}", tmp1 / 2);
}

fn num_of_factor2(a: usize) -> usize {
    let mut num = 0;
    let mut aa = a;
    while aa % 2 == 0 {
        aa /= 2;
        num += 1;
    }
    return num;
}

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

fn gcd(a: usize, b: usize) -> usize {
    if a < b {
        return gcd(b, a);
    }
    if b == 0 {
        return a;
    }
    return gcd(b, a - (a / b) * b);
}