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)

import java.io.BufferedReader
import java.io.IOException
import java.io.InputStreamReader
import java.io.PrintWriter
import java.util.*

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

private fun lcm(a: Long, b: Long): Long = a * b / gcd(a, b)

private fun solve() {
    val n = nextInt()
    val m = nextInt()
    val a = Array(n) { nextInt() }
    var l: Long = a[0].toLong()
    for (i in 1 until n) {
        l = lcm(l, a[i].toLong())
        if (l / 2 > m) {
            println(0)
            return
        }
    }
    l /= 2
    println((m - l) / l / 2 + 1)
}

fun main(args: Array<String>) {
    solve()
    out.close()
}

private var br = BufferedReader(InputStreamReader(System.`in`))
private var st: StringTokenizer? = null
private var out = PrintWriter(System.out)

@Throws(IOException::class)
private fun next(): String {
    while (st == null || !st!!.hasMoreTokens()) {
        st = StringTokenizer(br.readLine())
    }
    return st!!.nextToken()
}

@Throws(IOException::class)
private fun nextInt(): Int {
    return next().toInt()
}

@Throws(IOException::class)
private fun nextLong(): Long {
    return next().toLong()
}