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)

// x が半公倍数 for all k, a[k] * (p + 0.5)
//
// let b[k] = a[k]/2. Then
//   b[k], 3b[k], 5b[k], ...
//
// x は b[k] の奇数倍 => x を 2 で割り切る回数は全てで等しくないとダメ．
// b[k] = c[k] 2^e とする．
// c の gcd の奇数倍
//   
use proconio::input;
use num::integer::*;

fn div2(mut n: usize) -> usize {
  let mut e = 0;
  while n % 2 == 0 {
    n /= 2;
    e += 1;
  }
  e
}

fn main() {
  input! {
    n: usize,
    m: usize,
    a: [usize; n],
  }
  let e = div2(a[0]);
  if a.iter().all(|v| div2(v.clone()) == e) {
    let mut l = 1;
    for &v in &a { 
      l = lcm(l, v/2);
      if l > m { 
        break;
      }
    }
    println!("{}", m/l - m/(2*l));
  } else { 
    println!("0");
  }
}