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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <cmath>
#include <queue>
#include <set>
#include <map>
#include <iomanip>
#include <fstream>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int mod = 1000000007;

ll gcd(ll a, ll b) {
    while (b) {
        ll c = a % b;
        a = b;
        b = c;
    }
    return a;
}

int main() {
    ios::sync_with_stdio(false);
    int n, m;
    ll a[100005] = {}, g = 0;
    cin >> n >> m;
    for (int i = 0; i < n; i++) cin >> a[i];
    for (int i = 0; i < n; i++) {
        a[i] /= 2;
        ll b = gcd(g, a[i]);
        if (!g) g = a[i];
        else g = g * a[i] / b;
        if (g > mod) g = mod;
    }
    ll z = m / g;
    if (z % 2) cout << z / 2 + 1;
    else cout << z / 2;
}