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)

#pragma region cp-helper
#include <bits/stdc++.h>
using namespace std;
#define AC ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define ll long long
#define ull unsigned long long
#define ii pair<int, int>
#define lll pair<ll, ll>
#define vi vector<int>
#define vvi vector<vi>
#define vl vector<ll>
#define vll vector<lll>
#define vvl vector<vl>
#define vii vector<ii>
#define all(a) a.begin(), a.end()
#define qsort(a) sort(all(a))
#define qsortd(a) sort(all(a), greater<>())
#define qsortf(a, f) sort(all(a), f)
#define pb(n) push_back(n)
#define eb(n) emplace_back(n)
#define pp(a, b) emplace_back(make_pair(a, b))
#define umap unordered_map
#define nl '\n'
#define fileio(in, out) freopen(in, "r", stdin); freopen(out, "w", stdout)
#define qmod %mod
#define pls int
#define give main()
const int mod = 1000000007;
#pragma endregion

ll gcd (ll a, ll b) {
    if (b == 0) return a;
    return gcd(b, a%b);
}
ll lcm (ll a, ll b) {
    return (a/gcd(a, b))*b; 
}

ll n, m, aa, ans=1;

pls give {
    AC;
    cin >> n >> m;
    for (int i=0; i<n; i++) {
        cin >> aa;
        ans = lcm(ans, aa/2);
    }
    ans = m/ans;
    ans = ceil(ans/((double)2));
    cout << ans;
}