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;
#include<cstdlib>

#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)

int64_t gcd(int64_t a, int64_t b);
int64_t lcm(int64_t a, int64_t b);

int main(){
  int64_t n, m;
  cin >> n >> m;

  int guu=0;

  vector<int64_t> a(n);
  vector<int64_t> b(n);
  rep(i,n) {
    cin >> a.at(i);
    b.at(i) = a.at(i)/2;
    if(b.at(i)%2==0) guu++;
  }
  
  int64_t saidai;
  int64_t saisho = b.at(0);

  int64_t ans = 0;
  if(guu!=0&&guu!=n) cout << 0;
  else{
    for(int i=1; i<n; i++){
      saisho = lcm(saisho, b.at(i));
    }
  

  bool frag=true;
  
  rep(i,n){
    if((saisho/b.at(i))%2==0){frag=false; break;}
  }
  
  if(frag) cout<<(m/saisho)/2 + 1;
  else cout<<(m/saisho)/2;

}
}

int64_t gcd(int64_t a, int64_t b){
  if(a%b==0) return b;
  else return gcd(b, a%b);
}

int64_t lcm(int64_t a, int64_t b){
  return a*b/gcd(a,b);
}