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 Scala (2.11.7) (judge verdict: Accepted)

object Main extends App {
  val in = new java.util.Scanner(System.in)
  val N, M = in.nextInt
  val As = Array.fill(N)(in.nextLong)

  println(As.map(java.lang.Long.lowestOneBit).distinct.size match {
    case 1 => As.reduceLeft(lcm) match {
        case 0 => 0
        case m => (M / (m / 2) + 1) / 2
      }
    case _ => 0
  })

  def lcm(l: Long, r: Long): Long = {
    val ret = (l * r / gcd(l, r))
    if (ret > M * 2) 0 else ret
  }

  def gcd(l: Long, r: Long): Long = if (l % r == 0) r else gcd(r, l % r)
}