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)

"use strict"
function main(arg) {
    var data = arg.trim().split("\n")
    var m = data[0].split(" ").map(Number)[1]
    var _a = data[1].split(" ").map(Number).sort((a,b) => b - a)
    var a = _a.filter(function (x, i, self) {
        return self.indexOf(x) === i;
    });
    var base = a.shift()
    var records = []
    var ans = 0
    for (var p = 1; ; p++) {
        var x = base * (p + 0.5)
        if (x > m) {
            break
        }
        var has_error = false
        for (var i = 0; i < a.length; i++) {
            var _p = x / a[i] - 0.5
            if (! Number.isInteger(_p)) {
                has_error = true
                break
            }
        }
        if (!has_error) {
            ans++
        }
    }
    console.log(ans)
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));