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;

using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;


#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define all(x) (x).begin(),(x).end()
#define m0(x) memset(x,0,sizeof(x))

int dx4[4] = {1,0,-1,0}, dy4[4] = {0,1,0,-1};


int main()
{
    ll n,m;
    cin>>n>>m;
    vector<ll> a(n);
    for (ll i = 0; i < n; i++)
    {
        cin>>a[i];
    }
    ll lcm=1;
    for (ll i = 0; i < n; i++)
    {
        lcm=(lcm*a[i])/(__gcd(lcm, a[i]));
    }
    lcm/=2;
    cout<<(m/lcm)/2 + (m/lcm)%2<<endl;
    
    return 0;
}