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)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let v = read_vec::<i64>();
    let (n, m) = (v[0] as usize, v[1]);
    let a = read_vec::<i64>();

    let mut a0 = a[0];
    let mut count = 0;
    while a0 % 2 == 0 {
        a0 >>= 1;
        count += 1;
    }
    for i in 1..n {
        let mut a0 = a[i];
        let mut temp_count = 0;
        while a0 % 2 == 0 {
            a0 >>= 1;
            temp_count += 1;
        }
        if count != temp_count {
            println!("0");
            return;
        }
    }

    let a = a.into_iter().map(|x| x >> count).collect::<Vec<_>>();
    let m = m >> count - 1;

    let mut lcmnum = a[0];
    for i in 1..n {
        let gcdnum1 = gcd(lcmnum, a[i]);
        lcmnum = lcmnum / gcdnum1 * a[i];
        if lcmnum > m * 2 + 10 {
            println!("0");
            return;
        }
    }
    let all = m / lcmnum;
    let ans = (all + 1) / 2;
    println!("{}", ans);
}

fn gcd(a: i64, b: i64) -> i64 {
    if b == 0 {
        return a;
    }
    gcd(b, a % b)
}

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()
}