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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

// 最大公約数
ll gcd(ll m, ll n)
{
    if (n == 0)
        return m;
    else
        return gcd(n, m % n);
}

// 最小公倍数
ll lcm(ll a, ll b)
{
    return a / gcd(a, b) * b;
}
// https://yamakasa.net/atcoder-abc-150-d/
int main()
{
    int N;
    ll M;
    cin >> N >> M;

    ll a[N];
    ll b = 0;
    for (int i = 0; i < N; i++)
    {
        cin >> a[i];
        b = max(b, a[i] / 2);
    }

    ll l = 1;
    for (int i = 0; i < N; i++)
    {
        l = lcm(l, a[i] / 2);
        if (l > M)
        {
            cout << "0\n";
            return 0;
        }
    }

    for (int i = 0; i < N; i++)
    {
        ll t = l / (a[i] / 2);
        if (t % 2 == 0)
        {
            cout << "0\n";
            return 0;
        }
    }

    cout << (M - l) / (2 * l) + 1 << "\n";
    return 0;
}