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 (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
)

func main() {
	fmt.Println(resolve(parseProblem(os.Stdin)))
}

func parseProblem(r io.Reader) (int, int, []int) {
	const (
		initialBufSize = 100000
		maxBufSize     = 1000000
	)
	buf := make([]byte, initialBufSize)

	sc := bufio.NewScanner(r)
	sc.Buffer(buf, maxBufSize)
	sc.Split(bufio.ScanWords) // bufio.ScanLines
	n, m := scanInt(sc), scanInt(sc)
	var as []int
	for i := 0; i < n; i++ {
		as = append(as, scanInt(sc))
	}
	return n, m, as
}

func resolve(_, m int, as []int) int {
	l := 1
	for i := 0; i < len(as); i++ {
		if (as[i]/2)%2 == 0 {
			return 0
		}
		l = lcm(l, as[i]/2)
	}
	return ((m / l) + 1) >> 1
}

func lcm(a, b int) int {
	return a * b / gcd(a, b)
}
func gcd(a, b int) int {
	for b > 0 {
		t := a / b
		a, b = b, a-t*b
	}
	return a
}

// snip-scan-funcs
func scanInt(sc *bufio.Scanner) int {
	sc.Scan()
	i, _ := strconv.Atoi(sc.Text())
	return int(i)
}
func scanString(sc *bufio.Scanner) string {
	sc.Scan()
	return sc.Text()
}