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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;
int gcd(int a,int b){
	return b==0?a:gcd(b,a%b);
}
int main(){
	long long n,m,a,t=1,mx=0;
	cin>>n>>m;
	for(int i=0;i<n;i++){
		cin>>a;
		int g=gcd(a,t);
		if(mx==0){
			mx=1;
			while(!bool(a&(1<<mx-1))) mx++;
		} else {
			if(!(bool(a&(1<<mx-1)))||bool(a&(1<<(mx-1)-1))){
				cout<<"0\n";
				return 0;
			}
		}
		t=t/g*a;
		if(t>2*m){
			cout<<"0\n";
			return 0;
		}
	}
	cout<<(m+t/2)/t<<endl;
	return 0;
}