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
    
function gcd($a, $b) {
    if ($a < $b) list($a, $b) = [$b, $a];
    
    while($b > 0) {
        $_a = $b;
        $b = $a % $b;
        $a = $_a;
    }
    return $a;
}

function lcm($a, $b) {
    return $a * $b / gcd($a, $b);
}

sscanf(fgets(STDIN), '%d %d', $n, $m);
$ne = explode(' ', fgets(STDIN));

$lcmV = 1;
foreach($ne as $v) {
    $lcmV = lcm($lcmV, intval($v));
}

$base = $lcmV;

echo ceil($m / $lcmV);