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 _GLIBCXX_DEBUG
#define rep(i,n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int,int>;
long long GCD(long long a, long long b) {
    if (b == 0) return a;
    else return GCD(b, a % b);
}

long long LCM(long long a, long long b) {
    return a / GCD(a, b) * b;
}

int main()
{ ll n,m;
    cin>>n>>m;
  ll lcm=1;
    rep(i,n)
    {ll a;
    cin>>a;
    lcm=LCM(lcm,a);
    //cout << i<<endl;
    }
    if(n!=1)lcm/=2;
   // cout << lcm<<endl;
    ll count=0;
    for (ll i = 1; i*lcm <= m; i+=2)
    {
        count++;
      //  cout << i*lcm<<endl;
    }
    cout << count <<endl;
    return 0;
}