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: Wrong Answer)

#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<set>
#include<queue>
#include<cmath>
#define ll long long
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
static const int MAXN = 100000;
static const int MAX = 1000000000;

ll A[MAXN];

ll gcd(ll a, ll b)
{
   if (a%b == 0)
   {
       return(b);
   }
   else
   {
       return(gcd(b, a%b));
   }
}

ll lcm(ll a, ll b)
{
   return a * b / gcd(a, b);
}

int main(){
    int N, M;
    cin >> N >> M;
    ll a = 1;
    rep(i,N){
        cin >> A[i];
        A[i] /= 2;
        a = lcm(a,A[i]);
        if(a > MAX){
            cout << 0 << endl;
            return 0;
        }
    }
    ll ans = (a+M)/(2*a);

    cout << ans << endl;
 
    return 0;
}