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: Runtime Error)

import java.lang.Math

val MOD: Int = 1000000000 + 7
val MODL: Long = MOD.toLong()

fun main(args: Array<String>)
{
    val (n, m) = read().split(" ").map{it.toInt()}
    val a = read().split(" ").map{it.toInt() / 2}.toIntArray()

    var lcm = a[0]
    for (i in 1 until n) {
        lcm = lcm * a[i] / gcd(lcm, a[i])
    }

    var same = true
    for (i in 0 until n-1) {
        if (a[i] % 2 != a[i+1] % 2) {
            same = false
            break
        }
    }

    val num = m / lcm
    val ans = if (num == 0) num else (num+1)/2
    println(if (same) ans else 0)
}

fun gcd(a: Int, b: Int): Int {
    if (b == 0) return a

    return gcd(b, a % b)
}

fun read(): String = readLine()!!