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 <cstdio>
#include <iostream>
#include <string>
#include <vector>
#include <array>
#include <algorithm>
#include <utility>
#include <numeric>
#include <deque>
#include <stack>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <cmath>
#include <limits>
#include <cassert>
#include <bitset>

#define for0(i, N)    for (int i = 0  ; i <  (N); ++i)
#define for1n(i, N)   for (int i = 1  ; i <= (N); ++i)
#define for1(i, N)    for (int i = 1  ; i <  (N); ++i)
#define forn(i, N)    for (int i = 0  ; i <= (N); ++i)
#define forx(i, N, x) for (int i = (x); i <  (N); ++i)
#define forl(i, N, x, a) for (int i = (x), a = 0; a < (N);  \
                              i = (i + 1) % (N), ++a)

template<size_t i>
std::bitset<i> operator++(std::bitset<i> b, int){
    static_assert(i <= 64, "Cannot cast 64bit int.");
    return b = (unsigned long long)b + 1;
}

template<size_t i>
std::bitset<i> operator++(std::bitset<i> b){
    static_assert(i <= 64, "Cannot cast 64bit int.");
    auto temp = b;
    b++;
    return temp;
}

template<size_t i>
std::bitset<i> operator--(std::bitset<i> b, int){
    static_assert(i <= 64, "Cannot cast 64bit int.");
    return b = (unsigned long long)b - 1;
}

template<size_t i>
std::bitset<i> operator--(std::bitset<i> b){
    static_assert(i <= 64, "Cannot cast 64bit int.");
    auto temp = b;
    b--;
    return temp;
}

using namespace std;

typedef long long ll;
typedef long double ld;
typedef priority_queue<ll> pq;
typedef priority_queue<ll,vector<ll>, greater<ll>> pql;
typedef stack<ll> stk;
typedef queue<ll> qu;
typedef pair<ll, ll> pll;
typedef map<ll, ll> mll;
typedef unordered_map<ll, ll> umll;
typedef set<ll> sll;
typedef unordered_set<ll> usll;

ll gcd(ll a, ll b){
    if (a > b) return gcd(b, a);
    if (a == 0) return b;
    return gcd(b % a, a);
}

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

map<ll, ll> pf(ll x){
    ll y = x;
    ll a = 2;
    map<ll, ll> m;
    while (a * a <= x) {
        if (y % a == 0) {
            y /= a;
            ++m[a];
        } else {
            ++a;
        }
    }
    if (y != 1) ++m[y];

    return m;
}

ll p2(ll x){
    ll result = 0;
    while(!(x % 2)) x /= 2, result++;
    return result;
}

int main(void){
    cin.tie(0); ios::sync_with_stdio(false);
    ll n, m;
    cin >> n >> m;

    vector<ll> a(n), b(n), l(n);
    bool flag = false;
    for0(i, n){
        cin >> a[i];
        b[i] = a[i] / 2;
        l[i] = p2(a[i] / 2);
        if (i > 0 && l[i] != l[i - 1]) flag = true;
    }

    if (flag) {
        cout << 0;
        return 0;
    }

    int result = b[0];
    for1(i, n){
        result = lcm(result, b[i]);
    }

    cout << (result % 2 == 1 ? m / result / 2 + 1 : m / result/2);

    return 0;
}