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)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use proconio::input;
fn main() {
    input! {
        n: usize, m: i64,
        aa: [i64; n],
    }

    let bb: Vec<_> = aa.into_iter().map(|x| x/2).collect();
    // let zeros = bb[0].trailing_zeros();
    // if bb.iter().any(|&v| v.trailing_zeros() != zeros) {
    //     println!("0");
    //     return;
    // }

    let mut lcm = 1i64;
    for b in bb {
        let gcd = gcd(lcm, b);
        lcm = lcm / gcd * b;
        if (lcm / b) %2 == 0 {
            println!("0");
            return;
        }
    }
    // lcm * (2p-1) <= M  ...  p <= (M+lcm)/2lcm
    let ans = (m + lcm) / (lcm*2);
    println!("{}", ans);
}

fn gcd(x: i64, y: i64) -> i64 {
    if y == 0 {
        x
    } else {
        gcd(y, x % y)
    }
}