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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
)

func main() {
	var n, m int
	fmt.Scanf("%d %d", &n, &m)
	nums := make([]int, n)
	var lcm int
	var check int
	fmt.Scan(&nums[0])
	check = counter(nums[0])
	if n > 1 {
		fmt.Scan(&nums[1])
		lcm = nums[0] * nums[1] / GCD(nums[0], nums[1])
		if counter(nums[1]) != check {
			fmt.Println("0")
			return
		}
		for i := 2; i < n; i++ {
			fmt.Scan(&nums[i])
			lcm = LCM(lcm, nums[i])
			if counter(nums[i]) != check {
				fmt.Println("0")
				return
			}
		}
	} else {
		lcm = nums[0]
	}

	min := lcm / 2
	result := (m-min)/min/2 + 1
	fmt.Println(result)
}

func GCD(a, b int) int {
	for b != 0 {
		t := b
		b = a % b
		a = t
	}
	return a
}

func LCM(a, b int) int {
	result := a * b / GCD(a, b)

	return result
}

func counter(a int) int {
	result := 0
	for a%2 == 0 {
		result++
		a /= 2
	}
	return result
}