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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function main(input) {
  var N = input[0].split(" ")[0]-0;
  var M = input[0].split(" ")[1]-0;
  var list = input[1].split(" ").map(v=>v-0);
  var l = lcm(list);
  console.log(Math.trunc(M/(l/2)) - Math.trunc(M/l));
}

function lcm(args) {
    var a = args
    var g = (n, m) => m ? g(m, n % m) : n
    var l = (n, m) => n * m / g(n, m)
    var ans = a[0]

    for (var i = 1; i < a.length; i++) {
        ans = l(ans, a[i])
    }
    return ans
}
main(require('fs').readFileSync('/dev/stdin', 'utf8').trim().split("\n"))