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)

#include <iostream>
#include <iomanip>
#include <cassert>
#include <cstdint>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <array>
#include <deque>
#include <stack>
#include <queue>
#include <algorithm>
#include <functional>
#include <utility>
#include <cmath>
#include <numeric>
#include <sstream>

using namespace std;

#define DUMP(x) std::cerr << (#x) << " = " << (x) << "\n"
#define REP(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define EREP(i, a, b) for (int i = (int)(a); i <= (int)(b); ++i)
#define RREP(i, a, b) for (int i = (int)(a)-1; i >= (int)(b); --i)
#define rep(i, n) REP(i, 0, n)
#define erep(i, n) EREP(i, 0, n)
#define rrep(i, n) RREP(i, n, 0)
#define ALL(r) r.begin(), r.end()
#define YES cout << "YES\n"
#define Yes cout << "Yes\n"
#define NO cout << "NO\n"
#define No cout << "No\n"
#define M1 cout << "-1\n"
#define pb push_back
#define eb emplace_back
#define fi first
#define se second

template <typename T>
ostream &operator<<(ostream &os, vector<T> &v)
{
    os << "{";
    rep(i, v.size()) os << v[i] << (i == (int)v.size() - 1 ? "" : ", ");
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &p) { return (os << "(" << p.first << ", " << p.second << ")"); }
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &m)
{
    bool first = true;
    os << "{";
    for (const auto &e : m)
    {
        if (!first)
            os << ", ";
        os << "{" << e.first << ": " << e.second << "}";
        first = false;
    }
    os << "}";
    return os;
}
template <typename T>
ostream &operator<<(ostream &os, set<T> &s)
{
    os << "{";
    bool first = true;
    for (const auto &e : s)
    {
        if (!first)
            os << ", ";
        os << e;
        first = false;
    }
    os << "}";
    return os;
}
template <typename T>
T dup(T x, T y) { return (x + y - 1) / y; };
template <typename A, size_t N, typename T>
inline void arrayFill(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); }
template <class T>
inline bool chmax(T &a, T b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}
template <class T>
inline bool chmin(T &a, T b)
{
    if (a > b)
    {
        a = b;
        return true;
    }
    return false;
}
struct in
{
    const size_t n = 0;
    in() = default;
    in(size_t n) : n(n){};
    template <typename T>
    operator T()
    {
        T ret;
        cin >> ret;
        return ret;
    }
    template <typename T>
    operator vector<T>()
    {
        assert(n != 0);
        vector<T> ret(n);
        for (T &x : ret)
        {
            T tmp = in();
            x = tmp;
        }
        return ret;
    }
    template <typename T, typename U>
    operator pair<T, U>()
    {
        pair<T, U> ret;
        ret.first = in();
        ret.second = in();
        return ret;
    }
};

using ll = int64_t;
using vint = vector<int32_t>;
using vvint = vector<vint>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vstr = vector<string>;
using pint = pair<int32_t, int32_t>;
using vpint = vector<pint>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;
using setint = set<int32_t>;
using setstr = set<string>;
using qint = queue<int32_t>;
using qpint = queue<pint>;

constexpr std::int32_t INF = 1001001001;
constexpr std::int64_t LINF = 1001001001001001001;

ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

void Main()
{
    ll n = in(), m = in();
    vll a = in(n);
    ll ord2 = -1;
    rep(i, n)
    {
        ll cnt = 0;
        while (a[i] % 2 == 0)
        {
            a[i] /= 2;
            ++cnt;
        }
        if (ord2 == -1)
            ord2 = cnt;
        else if (ord2 != cnt)
        {
            cout << 0 << '\n';
            return;
        }

        if (ord2 == 1)
        {
            cout << 0 << endl;
            return;
        }
    }

    rep(i, ord2 - 1)
        m /= 2;
    ll l = 1;
    for (const auto e : a)
    {
        l = lcm(l, e);
        if (l > m)
        {
            cout << 0 << '\n';
            return;
        }
    }
    cout << dup(m, 2 * l) << '\n';
}

signed main()
{
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(15);
    Main();
    return 0;
}