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: Runtime Error)

#include <algorithm>
#include <cmath>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <string>
#include <vector>

using namespace std;
using LLONG = long long;
const LLONG MOD = 1000000007;

const LLONG GCM(LLONG a, LLONG b)
{
    if (b == 0) return a;
    return GCM(b, a % b);
}

const LLONG LCM(LLONG a, LLONG b)
{
    return a * b / GCM(a, b);
}

int main()
{
    LLONG N, M;
    cin >> N >> M;
    vector<int> As(N);
    for (int &Ai : As) cin >> Ai;
    LLONG lcm = LCM(As[0] / 2, As[1] / 2);
    for (int i = 2; i < N; ++i)
    {
        lcm = LCM(lcm, As[i] / 2);
    }
    if (M < lcm)
    {
        cout << 0 << endl;
    }
    else
    {
        cout << 1 + (M - lcm) / (lcm * 2) << endl;
    }
}