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: Accepted)

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

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pullull;
typedef pair<ll, int> plli;
typedef pair<int, pii> pipii;
typedef vector<vector<int> > mati;
typedef vector<vector<double> > matd;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
typedef vector<vector<vector<bool>>> vvvb;
typedef vector<pll> vpll;

#define FOR(i,x,y) for(ll i=(ll)x; i<(ll)y; ++i)
#define REP(i,y) FOR(i, 0, y)
#define RFOR(i,x,y) for(ll i=(ll)x; i>=(ll)y; --i)
#define RREP(i,x) RFOR(i, x, 0)
#define ALL(a) a.begin(), a.end()
#define pb push_back

inline void IN(void){
  return;
}

template <typename First, typename... Rest>
void IN(First& first, Rest&... rest){
  cin >> first;
  IN(rest...);
  return;
}

inline void OUT(void){
  cout << "\n";
  return;
}

template <typename First, typename... Rest>
void OUT(First first, Rest... rest){
  cout << first << " ";
  OUT(rest...);
  return;
}

template <typename T>
void vec_print(vector<T> VEC){
  REP(i, VEC.size()){
    cout << VEC[i] << " ";
  }
  cout << "\n";
};

template <typename T>
void mat_print(vector<vector<T> > MAT){
  REP(i, MAT.size()){
    REP(j, MAT[i].size()){
      cout << MAT[i][j] << " ";
    }
    cout << "\n";
  }
};

template <typename CLASS1, typename CLASS2>
class HOGE{
  public:
    CLASS1 key;
    CLASS2 value;
    HOGE(void){
      return;
    };
    HOGE(CLASS1 key, CLASS2 value){
      this->key = key;
      this->value = value;
    };
    ~HOGE(void){
      return;
    };

    void print(void){
      cout << "key : " << key << ", value : " << value << "\n";
      return;
    };
    
    bool operator==(const HOGE &obj){
      return (this->value == obj.value);
    };
    bool operator<(const HOGE &obj){
      return (this->value < obj.value);
    };
    bool operator>(const HOGE &obj){
      return (this->value > obj.value);
    };
};

template <typename CLASS1, typename CLASS2>
bool operator==(const HOGE<CLASS1, CLASS2> &hoge1, const HOGE<CLASS1, CLASS2> &hoge2){
  return hoge1.value == hoge2.value;
};

template <typename CLASS1, typename CLASS2>
bool operator<(const HOGE<CLASS1, CLASS2> &hoge1, const HOGE<CLASS1, CLASS2> &hoge2){
  return hoge1.value < hoge2.value;
};

template <typename CLASS1, typename CLASS2>
bool operator>(const HOGE<CLASS1, CLASS2> &hoge1, const HOGE<CLASS1, CLASS2> &hoge2){
  return hoge1.value > hoge2.value;
};

constexpr int INF = (1<<30);
constexpr ll INFLL = 1LL<<62;
constexpr long double EPS = 1e-12;
constexpr ll MOD = (ll)((1E+9)+7);

ll gcm(ll x, ll y){
  if(y==0) return x;
  return gcm(y, (x%y));
}

ll lcm(ll x, ll y){
  ll g = gcm(x, y);
  return y*(x/g);
}

int main(){
  cin.tie(0); // cut the cin and cout (default, std::flush is performed after std::cin)
  ios::sync_with_stdio(false); // cut the iostream and stdio (DON'T endl; BUT "\n";)

  ll N, M;
  IN(N,M);
  vll a(N);
  ll prod=1;
  REP(i,N){
    IN(a[i]);
    a[i]/=2;
  }
  sort(ALL(a));
  reverse(ALL(a));
  bool flag = false;
  REP(i,N){
    prod = lcm(prod, a[i]);
    if(prod>M) flag = true;
  }
  REP(i,N){
    if((prod/(a[i]))%2==0) flag = true;
  }
  //printf("%lld\n", prod);

  ll ans = M/prod;
  //printf("%lld\n", ans);
  ans = (ans+1)/2;

  if(flag){
    OUT(0);
    return 0;
  }

  OUT(ans);


  return 0;
}