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<bits/stdc++.h>
using namespace std;
#define ll long long
#define fastIO ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0)
int main()
{
    fastIO;
    ll n,m;
    cin>>n>>m;
    ll a[n],i,mul=1,gcd;
    for(i=0;i<n;i++)
    {
        cin>>a[i];
        mul*=a[i]/2;
    }
    ll lcm;
    lcm=a[0]/2;
    for(i=1;i<n;i++)
    {
        lcm=(lcm*a[i]/2)/__gcd(lcm,a[i]/2);
    }
    ll even=0,odd=0;
    for(i=0;i<n;i++)
    {
        if((a[i]/2)%2==0)
        {
            even++;
        }
        else
        {
            odd++;
        }   
    }
    if(even==0 || odd==0)
    {
        ll val2,ans;
        val2=m/lcm;
        ans=val2;
        if(odd==0)
        {
            ans-=floor(val2/2);
        }
        else
        {
            ans-=ceil(val2/2);
        }
        cout<<ans<<'\n';
    }
    else
    {
        cout<<0<<'\n';
    }
}