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 {
  def main(args: Array[String]): Unit = {
    val factors = io.StdIn.readLine.split(" ").map{_.toLong}
    val nums    = io.StdIn.readLine.split(" ").map{_.toLong}

    var least_common_multiple = 1L

    nums.foreach { i =>
      least_common_multiple *= i/2L/calcGcd(least_common_multiple, i/2L)
    }

    var count = 0
    var flag  = true

    while(flag) {
      val check_num = (2*count + 1)*least_common_multiple
      if(check_num <= factors(1)) count += 1
      else flag = false
    }

    println(count)

  }

    def calcGcd(num1: Long, num2: Long): Long = {
    var a = num1
    var b = num2
    if(a > b) {
      val tmp = a
      a = b
      b = tmp
    }
    var r = b%a

    while(r != 0L) {
      b = a
      a = r
      r = b%a
    }
    return a
  }
}