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: Accepted)

package main

import (
	"fmt"
	"os"
)

func main() {
	m, a := input()
	arr, b, f := toMulBinary(a)
	if !f {
		fmt.Println(0)
		os.Exit(0)
	}
	lcm := arrLCM(arr) * pow(b)
	count := m / lcm
	if count%2 == 0 {
		fmt.Println(count / 2)
	} else {
		fmt.Println(count/2 + 1)
	}
}

func arrLCM(a []int) int {
	n := 1
	for _, v := range a {
		n *= v / dcp(n, v)
	}
	return n
}

func dcp(p, q int) int {
	if q <= 0 {
		return p
	}
	return dcp(q, p%q)
}

func toMulBinary(a []int) ([]int, int, bool) {
	b := includBinary(a[0])
	for i := range a {
		n, f := isXBinary(a[i], b)
		if !f {
			return a, 0, false
		}
		a[i] = n
	}
	return a, b - 1, true
}

func pow(b int) int {
	return 1 << uint32(b)
}

func isXBinary(n, b int) (int, bool) {
	if n%pow(b) != 0 {
		return n, false
	}
	if n%pow(b+1) == 0 {
		return n, false
	}
	return n / pow(b), true
}

func includBinary(n int) int {
	c := 0
	for n != 1 {
		if n%2 == 1 {
			return c
		}
		n /= 2
		c++
	}
	return c
}

func input() (int, []int) {
	var n, m int
	fmt.Scan(&n, &m)
	a := make(map[int]bool, n)
	var t int
	for i := 0; i < n; i++ {
		fmt.Scan(&t)
		a[t] = true
	}
	sa := make([]int, 0, n)
	for i := range a {
		_, ok := a[i]
		if ok {
			sa = append(sa, i)
		}
	}
	return m, sa
}