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: Wrong Answer)

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val n = sc.nextInt
  val m = sc.nextLong
  val seq = Seq.fill(n)(sc.nextLong)
  
  def gcd(a: Long, b: Long): Long = {
    if (b == 0) a
    else gcd(b, a % b)
  }
  
  def lcm(a: Long, b: Long) = a * b / gcd(a, b)
  def multiLcm(seq: Seq[Long]) = seq.reduce(lcm)

  val cm = multiLcm(seq.map(_ / 2)).toInt
  
  println(Stream.from(cm, cm * 2).takeWhile(_ <= m).size)
}