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 {

  def gcd(a: Long, b: Long): Long = if (b == 0)
    a
  else
    gcd(b, a % b)

  def lcm(a: Long, b: Long): Long = a * b / gcd(a, b)

  def lcm(list: Seq[Long]): Long = list.reduceLeft(lcm)

  def countDivide2(a: Long, acc: Int): Int = if (a % 2 == 0)
    countDivide2(a / 2, acc + 1)
  else
    acc

  val Array(_, m) = io.StdIn.readLine().split(' ').map(_.toLong)
  val a = io.StdIn.readLine().split(' ').map(_.toLong).distinct

  val answer = if (a.map(countDivide2(_, 0)).distinct.size != 1)
    0
  else {
    val lcmHalf = lcm(a.map(_ / 2))
    math.ceil((m / lcmHalf).toDouble / 2.0)
  }

  println(answer.toLong)
}