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 (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter

fun main() {
    PrintWriter(System.out).use { out ->
        solve(out)
        out.flush()
    }
}

fun solve(out: PrintWriter) {
    val (n, m) = readLongList()
    val aList = readLongList()

    val divCount = countDiv(aList.first(), 2)
    for (a in aList.drop(1)) {
        val count = countDiv(a, 2)
        if (divCount != count) {
            println(0)
            return
        }
    }

    var t = aList.first() / 2
    for (a in aList) {
        t = lcm(t, a / 2)
    }

    println((m / t + 1) / 2)
}


/** O(log(n)) */
tailrec fun countDiv(n: Long, divisor: Long, count: Long = 0L): Long =
    if (n % divisor == 0L) countDiv(n / divisor, divisor, count + 1) else count

/** O(log(n)): n = min(a, b) */
tailrec fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)

/** O(log(n)): n = min(a, b) */
fun lcm(a: Long, b: Long) = a / gcd(a, b) * b

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)