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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

fun main(args: Array<String>) {
    fun gcd(a: Long, b: Long): Long {
        return if (b > 0) gcd(b, a % b) else a
    }

    fun lcm(a: Long, b: Long): Long {
        return a * b / gcd(a, b)
    }
    val (N, M) = readLine()!!.split(" ").map(String::toLong)
    val AN = readLine()!!.split(" ").map(String::toLong)

    // 最小公倍数でMを超えたら答えは0
    var l = 1L
    for (i in AN.map { it / 2 }) {
        l = lcm(l, i)
        if (l > M) {
            println(0)
            return
        }
    }

    println(((M / l) + 1) / 2)
}