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: Runtime Error)

object Main extends App{
  // aとbの最大公約数を求める
  def gcd(a:Int,b:Int):Int ={
    var x,y = 0
    if( a > b){x = a; y=b}
    else{x = b;y=a}
    while( x % y != 0){
        val t = x % y
        x = y;y = t
    }
    y
  }
  // aとbの最小公倍数を求める。
  def lcm(a:Int,b:Int):Int ={
    a * b / gcd(a,b)
  }
  // 整数nが2で何回割れるかを返す
  def f( n:Int):Int ={
    var cnt = 0
    var tmp = n
    while( tmp % 2 == 0 ){
        cnt += 1
        tmp = tmp / 2
    }
    cnt
  }
  
  val List(n,m) = readLine.split(" ").map(_.toInt).toList
  val a = readLine.split(" ").map(_.toInt).toSet
  if(a.map(f).size == 1){
    val lcm_v = a.map(_/2).reduce(lcm) // 数列a/2の最小公倍数
    println( m / lcm_v / 2 + 1)
  }else{
    println("0")
  }
}