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.*
import java.util.*

fun solve(N: Long, M: Long, a: LongArray){
    val g = a.toSet().map{ it / 2L }.reduce{ a, b -> a / gcd(a,b) * b }
    // 1 <= g * (2*m - 1) <= M
    // m = 1, 2, 3, ... , (M / g + 1) / 2
    println((M/g +1) / 2)
    return
}

fun gcd(x: Int, y: Int): Int = if (y == 0) x else gcd(y, x % y)
fun gcd(x: Long, y: Long): Long = if (y == 0L) x else gcd(y, x % y)

fun main(args: Array<String>) {
    fun StringArray(size: Int, init: (Int) -> String = { "\u0000" }): Array<String> {
        return Array<String>(size, init)
    }
    class Scanner(stream: InputStream) {
        private val reader = BufferedInputStream(stream).bufferedReader()
        private var st: StringTokenizer? = null
        fun next(): String {
            while (!(st?.hasMoreTokens() ?: false)) st = StringTokenizer(reader.readLine())
            return st!!.nextToken()
        }
    }
    val sc = Scanner(System.`in`)
    val N = sc.next().toLong()
    val M = sc.next().toLong()
    val a = LongArray(N.toInt())
    for (i in 0 until N.toInt()) {
        a[i] = sc.next().toLong()
    }
    solve(N, M, a)
}