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.util.*

// Greatest Common Divisor
fun gcd(a: Int, b: Int): Int = if (b == 0) a else gcd(b, a % b)
fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)

// Least Common Multiple
fun lcm(a: Int, b: Int): Int = a * b / gcd(a, b)
fun lcm(numbers: Iterable<Int>): Int = numbers.fold(1) { acc, n -> lcm(acc, n) }

fun main(args: Array<String>) {
    val result = solve(Scanner(System.`in`))
    if (result.isNotEmpty()) println(result)
}

fun solve(`in`: String) = solve(Scanner(`in`))

fun solve(sc: Scanner): String {
    val N = sc.nextInt()
    val M = sc.nextInt()
    val A = (1..N).map { sc.nextInt() + 1 }

    val A2 = A.map { it / 2 }
    if (A2.filter { it % 2 == 0 }.count() > 0) {
        return "0"
    }

    val lcm = lcm(A2)
    var i = 1
    var n = 0
    while (i * lcm <= M) {
        n++
        i += 2
    }

    return n.toString()
}