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: Runtime Error)

package main

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

var sc = bufio.NewScanner(os.Stdin)

func nextint() int{
	sc.Scan()
	i,_ := strconv.Atoi(sc.Text())
	return i
}

func main() {
	sc.Split(bufio.ScanWords)
	n := nextint()
	m := nextint()
	a := make([]int,n)
	for i := 0; i < n; i++ {
		a[i] = nextint()
	}

	b := make([]int,m+1)
	for _,s := range a {
		for t := 1; t <= m; t++ {
			if !(t >= s/2 && (t-s/2)%s == 0) {
				b[t] = 1
			}
		}
	}
	
	res := 0
	for i := 1; i <= m; i++ {
		if b[i] == 0 {
			res ++
		}
	}
	fmt.Println(res)
}