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 int long long
using namespace std;

int gcd(int a, int b) {
  if (b == 0)
    return a;
  return gcd(b, a % b);
}

int lcm(int a, int b) {
  int x = gcd(a, b);
  return (a / x) * b;
}

signed main() {
  int N, M;
  cin >> N >> M;
  vector<int> a(N);

  sort(a.begin(), a.end());

  int l = 1;
  for (int i = 0; i < N; i++) {
    cin >> a[i];
    if ((a[i] / 2) / gcd(a[i] / 2, l) > M / l || l < 0) {
      cout << 0 << endl;
      return 0;
    }
    l = lcm(l, a[i] / 2);
  }

  int x = M / l + 10000000;
  if (x % 2 == 0) {
    x++;
  }

  for (int i = x; i >= 1; i -= 2) {
    if (i * l <= M) {
      cout << (i + 1) / 2 << endl;
      return 0;
    }
  }

  cout << 0 << endl;
  return 0;
}