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 rep(i, n) for (int i = 0; i < (n); i++)
#define repi(i, s, n) for (int i = (s); i < (n); i++)
#ifdef LOCAL
#define INPUT_FILE                   \
  ifstream in("abc150/abc150_d.txt"); \
  cin.rdbuf(in.rdbuf());
#else
#define INPUT_FILE
#endif
#define CIN_OPTIMIZE \
  cin.tie(0);        \
  ios::sync_with_stdio(false);
typedef pair<int, int> P;
typedef long long ll;
const int INF = 100100100;
const int MOD = 1e9 + 7;

ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

int main() {
  INPUT_FILE CIN_OPTIMIZE;

  int N;
  ll M;
  cin >> N >> M;
  
  vector<ll> a(N);
  rep(i, N) { cin >> a[i]; }

  ll l = 1;
  rep(i, N) { l = lcm(l, a[i]/2); }

  ll cnt = 0;
  while (l * (2 * cnt + 1) <= M) {
    cnt++;
  }

  cout << cnt << endl;
}