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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN,"%d %d",$n,$m);
$a = explode(" ",fscanf(STDIN,"%s",$s));
$x = 0;
$p = 0;
$temp = 0;
$result = array();

function is_decimal($value) {
  return filter_var($value, FILTER_VALIDATE_INT) !== false;
}


foreach($a as $ak){
  for($p=0; (int)$ak * ($p + 0.5) <= $m; $p++){
    $temp = (int)$ak * ($p + 0.5);
    if(is_decimal($temp) && $temp >= 1 && $temp <= $m) {
      $result[] = (int)$temp;
     
    }
  }
}
$output = array_count_values($result);
$count = 0;
foreach($output as $value){
  if($value == 2){
    $count++;
  }
}
echo $count;

  ?>