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>) {
    var (N, M) = readInputLine().split(" ").map { it.toLong() }
    val aArr = readInputLine().split(" ").map { it.toLong() / 2L }.toLongArray()

    var divPow = 1L
    var divTmp = aArr[0]
    while (divTmp % 2L == 0L) {
        divPow *= 2L
        divTmp /= 2L
        M /= 2L
    }
    if (aArr.any { it % divPow != 0L }) {
        println(0)
        return
    }
    for (i in 0 until N.toInt()) {
        aArr[i] /= divPow
    }

    var lcm = aArr[0]

    for (a in aArr) {
        val gcd = gcd(lcm, a)
        lcm = lcm / gcd * a
        if (lcm > M) {
            println(0)
            return
        }
    }

    val ans = if (M / lcm % 2L == 0L) M / lcm / 2L else M / lcm / 2L + 1L

    println(ans)
}

fun readInputLine(): String {
    return readLine()!!
}

fun gcd(a: Long, b: Long): Long {
    if (b > a) {
        return gcd(b, a)
    }
    if (b == 0L) {
        return a
    }
    return gcd(b, a % b)
}