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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define _overload3(_1,_2,_3,name,...) name
#define _rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(ll i=ll(a);i<ll(b);++i)
#define rep(...) _overload3(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)
#define inf (ll)1e9
#define mod (ll)(1e9+7)
#define d(x) cerr<<#x<<"="<<x<<endl;
#define p(x) cout<<(x)<<endl
#define ps(x) cout<<(x);
#define pk(x) cout<<(x)<<" ";
#define pfix(d,x) cout << fixed << setprecision(d) << x << endl;
#define pb push_back
#define all(v) (v).begin(), (v).end()
#define minel(v) *min_element(all(v))
#define minind(v) distance((v).begin(), min_element(all(v)))
#define maxel(v) *max_element(all(v))
#define maxind(v) distance((v).begin(), max_element(all(v)))
#define p2d(v,n,m) rep(i,n){rep(j,m){pk(v[i][j]);}p("");}
#define fi first
#define se second
template<typename A, size_t N, typename T>
void Fill(A (&array)[N], const T &val){
    std::fill( (T*)array, (T*)(array+N), val );
}
ll a[100001],b[100001],c[100001],d,n,m,x,y,z,h,w,k,sum,mi=inf,ma=-inf,ans,s,t,l,r,res,tmp,itr,p,q;
bool flag;
int dx[4]={1,0,-1,0},dy[4]={0,1,0,-1};
int dx8[8]={1,1,0,-1,-1,-1,0,1},dy8[8]={0,1,1,1,0,-1,-1,-1};
char cha;
string st;
typedef map<ll, ll> imap;
typedef pair<ll, ll> P;
typedef vector<int> VI;
typedef vector<ll> VL;
typedef vector<pair<ll,ll> > VP;
P pa;

ll gcd(ll a, ll b)
{
    if (a < b) {
        a ^= b;
        b ^= a;
        a ^= b;
    }
    return b ? gcd(b, a % b) : a;
}

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



int main(){
    cin>>n>>m;
    ll L=1;
    rep(i,n){
        cin>>a[i];
        L=lcm(L,a[i]/2);
    }
    rep(i,2*m){
        if(L*(2*i+1)<=m)sum++;
        else break;
    }
    p(sum);
    return 0;
}