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 == 0L) a else gcd(b, a % b)
    }

    fun lcm(a: Long, b: Long): Long {
        return a / gcd(a, b) * b
    }

    val (n, m) = readLine()!!.split(' ').map { it.toInt() }
    val a = readLine()!!.split(' ').map { it.toLong() }

    fun f(x: Long): Int {
        var y = x
        var cnt = 0
        while (y % 2 == 0L) {
            cnt++
            y /= 2L
        }
        return cnt
    }
    
    if (a.map { f(it) }.toSet().size != 1) {
        println(0)
        return
    }
    
    val x = a.map { it / 2 }.reduce { acc, l -> lcm(acc, l) }

    var ans = 0

    var j = 1L
    while (x * j <= m) {
        ans++
        j += 2
    }

    println(ans)
}