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;
fn helper(mut v: usize) -> usize {
  let mut ret = 0;
  while v % 2 == 0 {
    v /= 2;
    ret += 1;
  }
  ret
}

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

fn lcm(a: usize, b: usize) -> usize {
  a * b / gcd(a, b)
}

fn main() {
  input! {
    n: usize,
    mut m: usize,
    mut ais: [usize;n] 
  }
  
  for i in 0..ais.len() {
    if ais[i] % 2 == 1 {
      println!("0");
      return
    }
    ais[i] /= 2;
  }
  
  let t = helper(ais[0]);
  for i in 0..ais.len() {
    if helper(ais[i]) != t {
      println!("0");
      return
    }
    ais[i] >>= t;
  }
  m >>= t;

  let mut lcm_val = 1;
  for i in 0..ais.len() {
    lcm_val = lcm(lcm_val, ais[i]);
    if lcm_val > m {
      println!("0");
      return
    }
  }
    
  let mut result = m / lcm_val; 
  result = (result + 1) / 2;
  
  println!("{}", result);
}