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;
const int N=1e5+5;
int n;
ll m,a[N],b[N];
int main()
{
    scanf("%d%lld",&n,&m);
    for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
    sort(a+1,a+1+n);
    ll p=1,s=1;
    for(int i=1;i<=n;i++)
    {
        b[i]=a[i]/2;
        p=p/__gcd(p,(ll)b[i])*b[i];
        s=s/__gcd(s,(ll)a[i])*a[i];
        if(p>m||s>m)
        {
            printf("0\n");return 0;
        }
    }
    for(int i=1;i<=n;i++)
        if(p/b[i]%2==0)
            {printf("0\n");return 0;}
    int l=0,r=m/s,ans;
    assert(p<=m);
    while(l<=r)
    {
        int mid=l+r>>1;
        if(s*mid+p<=m) ans=mid,l=mid+1;
        else l=mid-1;
    }
    printf("%d\n",ans+1);
}