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 all(v) ((v).begin()),((v).end())
#define ll long long
#define fastIO cout << fixed << setprecision(12), ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr)
double const EPS = 1e-12, PI = acos(-1);
const int N = 1e6 + 9, M = 5e3 + 9, OO = 1e9 + 7, MOD = 1e9 + 7;
const ll inf = 1e18;

ll arr[N], a[N];
ll pre[N];

int main() {
  fastIO;
#ifdef LOCAL
  freopen("input.in", "rt", stdin);
#endif
  int n;
  ll m;
  cin >> n >> m;
  for (int i = 0; i < n; ++i) {
    cin >> arr[i];
    arr[i] /= 2;
  }
  ll ans = arr[0];
  for (int i = 1; i < n; i++)
      ans = (((arr[i] * ans)) / (__gcd(arr[i], ans)));
//  cerr << ans << endl;
  m /= ans;
  cout << ((m+1) / 2ll);
//  cout << (m / ans) + (m % ans != 0);
  return 0;
}