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)

use std::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

struct UnionFind{
    v: Vec<usize>
}

fn gcd(a: u64, b: u64) -> u64{
    if b == 0{
        return a;
    }

    return gcd(b, a%b);
}

fn lcm(a: u64, b: u64) -> u64{
    return (a*b)/ gcd(a, b);
}

fn main(){
    let line: Vec<usize> = read_as_vec();
    let (n, m) = (line[0], line[1] as u64);

    let a: Vec<u64> = read_as_vec();
    let mut lcm_of_vec = a[0];

    for &elem in &a{
        if lcm_of_vec%elem == 0 && (lcm_of_vec/elem%2) == 0{
            println!("0");
            return;
        }else if elem%lcm_of_vec == 0 && (elem/lcm_of_vec%2) == 0{
            println!("0");
            return;
        }
        lcm_of_vec = lcm(elem, lcm_of_vec);
        if lcm_of_vec > 2*m{
            println!("0");
            return;
        }
    }
    let half_lcm: u64 = lcm_of_vec/2;

    if half_lcm > m as u64{
        println!("0");
    }else{
        println!("{}", (m + half_lcm)/lcm_of_vec);
    }
}