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: Accepted)

#include <bits/stdc++.h>
#define INF 1000000000000001
#define ll long long
using namespace std;

int main()
{
  ll N, M;
  cin >> N >> M;
  ll a;
  ll lcm = 1;
  for (ll i = 0; i < N; ++i)
  {
    cin >> a;
    a /= 2;
    lcm = lcm * (a / __gcd(lcm, a));
    if ((lcm / a) % 2 == 0)
    {
      cout << 0 << endl;
      return 0;
    }
    if (lcm > M)
    {
      cout << 0 << endl;
      return 0;
    }
  }
  ll ans = M / lcm;
  // cout << ans << endl;
  ans = ans / 2 + (ans % 2);
  cout << ans << endl;
}