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>
#define ll long long
#define ld long double
#define endl "\n"
using namespace std;

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

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.precision(10);

    ll n,k;
    cin >> n >> k;
    ll cost[n];
    ll input[n];
    for (ll i=0;i<=n-1;i++)
    {
        cin >> input[i];
        cost[i]=input[i]/2;
    }

    ll ans=1;
    for (ll i=0;i<=n-1;i++)
    {
        ans=lcm(cost[i],ans);
    }

    for (int i=0;i<=n-1;i++)
    {
        if (ans%input[i]==0)
        {
            cout << "0" << endl;
            return 0;
        }
    }

    k=k-ans;
    if (k>=0)
    {
        ll val=1+(k/(2*ans));
        cout << val << endl;
    }
    else
    {
        cout << "0" << endl;
    }
    
    return 0;
}