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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define ll long long int
#define dbg(x) cout<<"( "<<#x<<" -> "<<x<<" )"<<endl;
using namespace std;
ll gcd(ll a1,ll b1)
{
    if (b1==0LL)
    return a1;
    return (gcd(b1,a1%b1));
}
int main()
{
    int n,m;
    scanf("%d%d",&n,&m);
    int a[n];
    ll g,lcm;
    for (int i=0;i<n;i++)
    {
        scanf("%d",&a[i]);
        if (i==0)
        lcm=a[i];
        else
        {
            g=gcd(lcm,1LL*a[i]);
            lcm=(lcm*a[i])/g;
        }
    }
    lcm=lcm/2LL;
    ll val=m/lcm;
    ll ans=0LL;
    if (val%2==0)
    ans=(val/2LL);
    else
    ans=(val/2LL)+1;
    printf("%lld\n",ans);
    return 0;
}