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;

long long gcd(long long a,long long b){
  long long r,tmp;

  if(a<b){
    tmp = a;
    a = b;
    b = tmp;
  }
 
  r = a % b;
  while(r!=0){
    a = b;
    b = r;
    r = a % b;
  }
  return b;
}

int main(){
  int n,m;
  cin >> n >> m;
  long long lcmi;
  cin >> lcmi;
  lcmi /= 2;
  long long tmp = lcmi;

  int cnt=0;
  while(tmp%2!=1){
    tmp/=2;
    cnt++;
  }

  for (int i = 1; i < n; i++)
  {
    long long a;
    cin >> a;
    a /= 2;
    
    tmp = a;
    int cnt2 = 0;
    while(tmp%2!=1){
      tmp/=2;
      cnt2++;
    }
    if(cnt!=cnt2){
      cout << 0 << endl;
      return 0;
    }
    lcmi = a*lcmi/gcd(lcmi,a);
  }
  
  int b = 0;
  int ans = 0;
  tmp = lcmi;
  while(lcmi <= m){
    if(b%2 == 0){
      ans++;
    }
    lcmi+=tmp;
    b++;
  }
  cout << ans << endl;  
}