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)

use proconio::input;
use num::integer::lcm;

fn f(mut x: i64) -> i64 {
  let mut y = 0;
  while (x & 1) == 0 {
    y += 1;
    x >>= 1;
  }
  y
}

fn main() {
  input! {
    n: i64, m: i64,
    a: [i64; n],
  };
  let a: Vec<i64> = a.iter().map(|x|x/2).collect();
  
  let l = a.iter().fold(1, |x, &y| lcm(x, y));
  
  let y = f(a[0]);
  if !a.iter().all(|&x| y == f(x)) {
    println!("0");
  } else {
    let cnt = m / l;
    let ans = (cnt + 1) / 2;

    println!("{}", ans);
  }
}