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: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main() {
  int n, m, tmp;
  cin >> n >> m;
  vector<int> a, aHalf;
  for (int i = 0; i < n; i++) {
    cin >> tmp;
    a.push_back(tmp);
  }
  std::sort(a.begin(),a.end(),std::greater<int>());

  for (int i = 0; i < n; i++) {
    aHalf.push_back(a.at(i) / 2);
  }

  int count = 0;
  int half = (a.at(0) / 2);
  int check = 1;
  for (int x = half; x <= m; x += a.at(0)) {
    check = 1;
    for (int i = 1; i < n; i++) {
      if (a.at(i) == a.at(0)) continue;
      if ((x - aHalf.at(i)) % a.at(i) != 0) {
        check = 0;
        break;
      }
    }
    if (check == 1) count++;
  }

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