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 <vector>
#include <algorithm>
using namespace std;

#define REP(i, n) for(int i = 0; i < (int)(n); ++i)
#define FOR(i, m, n) for(int i = (int)(m); i < (int)(n); ++i)

// Greatest Common Multiple (GCD)
// 2数の最大公約数 by ユークリッド互助法
template <typename T=long long>
T gcd(T a, T b)
{
    if(b == 0) return a;
    else return gcd(b, a % b);
}

// Least Common Multiple (LCM)
// 2数の最小公倍数
template <typename T=long long>
T lcm(T a, T b) {return a * b / gcd( a, b );}

int main()
{
    int N, M;
    cin >> N >> M;
    vector<long long> a(N);
    REP(i, N) cin >> a[i];

    long long ans = 0, LCM = 1;
    REP(i, N){
        a[i] = a[i]/2;
        LCM = lcm<long long>(LCM, a[i]);
        if(a[i]%2 == 0 or LCM > M){
            cout << 0 << endl;
            return 0;
        }
    }
    cout << (M/LCM+1)/2 << endl;

    return 0;
}