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: Runtime Error)

use std::io::{self, BufRead};
use std::collections::HashMap;

pub fn find_prime_factors(n: i64) -> HashMap<i64, i64> {
  let mut res = HashMap::new();
  let mut i = 2;
  let mut m = n;
  while i * i <= m {
    while m % i == 0 {
      let val = 1 + res.get(&i).unwrap_or(&0);
      res.insert(i, val);
      m /= i;
    }
    i += 1
  }
  if m != 1 {
    let val = 1 + res.get(&m).unwrap_or(&0);
    res.insert(m, val);
  }
  res
}

pub fn merge(x: &mut HashMap<i64, i64>, y: &HashMap<i64, i64>) {
  for (p, n) in y {
    let o = x.get(p).map(|q| *q);
    if let Some(q) = o {
      if q < *n {
        x.insert(*p, *n);
      }
    } else {
      x.insert(*p, *n);
    }
  }
}

fn main() {
  let stdin = io::stdin();
  let mut lines = stdin.lock().lines();
  let line = lines.next().unwrap().unwrap();
  let vs: Vec<i64> = line.split(' ').map(|x| x.parse().unwrap()).collect();
  let n = vs[0];
  let m = vs[1] * 2;
  let line = lines.next().unwrap().unwrap();
  let xs: Vec<i64> = line.split(' ').map(|x| x.parse().unwrap()).collect();
  let mut lcm = find_prime_factors(xs[0]);
  for i in 1..n {
    merge(&mut lcm, &find_prime_factors(xs[i as usize]));
  }
  let lcm: i64 = lcm.iter().map(|(p, n)| p * n).product();
  let count = (m / lcm + 1) / 2;
  println!("{}", count);
}