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 (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func main() {
	var N, M int
	fmt.Scan(&N, &M)

	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	A := make([]int, N)
	for i := 0; i < N; i++ {
		sc.Scan()
		A[i], _ = strconv.Atoi(sc.Text())
		A[i] /= 2
	}

	pow := -1
	for _, a := range A {
		c := 0
		for a > 0 && a%2 == 0 {
			a /= 2
			c++
		}
		if pow < 0 {
			pow = c
		}
		if pow != c {
			fmt.Println(0)
			return
		}
	}

	g := A[0]
	t := A[0]
	for i := 1; i < N; i++ {
		a := A[i]
		g = gcd(a, g)
		t = lcm(a, t)
	}
	count := 0
	for i := 1; t*i <= M; i += 2 {
		count++
	}
	fmt.Println(count)
}

func lcm(a, b int) int {
	return a * b / gcd(a, b)
}

func gcd(a, b int) int {
	if a < b {
		b, a = a, b
	}

	for b != 0 {
		t := b
		b = a % b
		a = t
	}
	return a
}