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 Array(n, m) = scala.io.StdIn.readLine.split(" ").map(_.toInt)
  val a = scala.io.StdIn.readLine.split(" ").map(_.toInt)
  val aa = a.distinct
  if (aa.forall(aa => aa % 2 == 0)) {
    var aaa = aa(0) / 2
    var aalist = List[Int]()
    while (aaa <= m) {
      // println(aaa)
      aalist :+= aaa.toInt
      aaa += a(0)
      //      println(aaa)
    }
   // println(aalist)
    aa.tail.foreach { tmpa =>
      // println("tempa=" + tmpa)

      aalist = aalist.filter { tmpaa =>
        //println("tmpaa=" + tmpaa)
        //println((tmpaa.toFloat / tmpa))
        (tmpaa.toFloat / tmpa) * 10 % 10 == 5
      }
    }
    println(aalist.length)
  } else {
    println(0)
  }

}