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)

#import<bits/stdc++.h>
using namespace std;
using Int = long long;
template<class T> T gcd(T a,  T b) {return b ? gcd(b, a % b) : a;}
template<class U> U lcm( U m, U n ){if((0 == m )||( 0 == n ))return 0; return ((m / gcd(m, n)) * n); }
int main(){
    Int N, M;
    cin >> N >> M;
    vector<Int>a(N);
    for(auto& e : a) cin >> e;
    for(auto& e : a) e /= 2;
    Int cm = accumulate(a.begin(),a.end(),1LL,[](Int lc, Int e){return lcm(lc,e);});
    cout << max(0LL,(M / cm) / 2 + ((M / cm) % 2 == 0 ? -1  : + 1))<< endl;
}