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: Time Limit Exceeded)

tailrec fun gcd(a: Long, b: Long): Long {
    return when {
        a < b -> {
            gcd(b, a)
        }
        b == 0L -> {
            return a
        }
        else -> {
            gcd(b, a % b)
        }
    }
}

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

fun main(args: Array<String>) {
    val (n, m) = readLine()?.split(" ")?.map(String::toLong) ?: return
    val aList = readLine()?.split(" ")?.map(String::toLong)?.distinct() ?: return
    aList.map {
        var r = it
        var count = 0
        while (true) {
            if (r % 2 == 0L) {
                count++
                r /= 2
            } else {
                return@map count
            }
        }
    }.distinct().size.apply {
        if (this != 1) {
            println(0L)
            return
        }
    }

    //最小公倍数を求めて割る
    val ak2 = aList.map { it / 2 }.reduce { a, b -> lcm(a, b) }
    val ak = aList.reduce { a, b -> lcm(a, b) }
    val count = m / ak2 - m / ak
    println(count)
}