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: Accepted)

var R = mutableListOf<String>()
fun main(args: Array<String>) {
    val (N, M) = listOfLong()
    val A = listOfLong().map { a -> a / 2 }
    val s = A.reduce { acc, a -> lcm(acc, a) }
    if (A.any { a -> (s / a) % 2 == 0L }) {
        println(0)
        return
    }
    var ans = 0L
    var S = s
    while (S <= M) {
        ans += 1
        S += s * 2
    }
    println(ans)
}
fun next() = readLine()!!
fun listOfString() = next().split(" ")
fun listOfLong(delta: Long = 0L) = listOfString().map { java.lang.Long.parseLong(it) + delta }
fun gcd(a: Long, b: Long): Long = if (b > 0) gcd(b, a % b) else a
fun lcm(a: Long, b: Long): Long = a / gcd(a, b) * b