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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#include<algorithm>
typedef long long ll;
#define INF 1LL<<62
#define inf 1000000007

ll dep(ll a,ll b){
	if(b==0){
		return a;
	}
	return dep(b,a%b); 
}
int main() {
	ll n,m;
	cin>>n>>m;
	ll ch[100010];	ll cnt2[100010];
	for(ll i=0;i<n;i++){
		ll x;
		cin>>x;
		x/=2;
		ll sum=0;
		while(x%2==0){
			sum++;
			x/=2;
		}		cnt2[i]=sum;
		ch[i]=x;
	}
	ll sum2=cnt2[0];
	for(ll i=0;i<n-1;i++){
		if(cnt2[i]!=cnt2[i+1]){
			cout << 0;
			return 0;
		}
		sum2=max(sum2,cnt2[i+1]);
	}
	for(ll i=0;i<sum2;i++){
		m/=2;
	}
	ll lcm=ch[0];
	for(ll i=0;i<n;i++){
		ll now=ch[i];
		ll gcd=dep(max(lcm,now),min(lcm,now));
		lcm=lcm/gcd*now;
		if(lcm>m){
			cout << 0;
			return 0;
		}
	}

//	cout << gcd<<endl;
//	cout << GCD<<endl;

	cout <<(m/lcm-1)/2+1;
	// your code goes here
	return 0;
}