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: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
ll gcd(ll a,ll b)
{
	return b==0?a:gcd(b,a%b);
}
ll lcm(ll a,ll b)
{
	return a*b/gcd(a,b);
}
ll a[100006];
int main(){
    ll n,m;
    scanf("%lld%lld",&n,&m);
    int lcm1=1;
    for(int i=1;i<=n;i++){
        scanf("%lld",&a[i]);
        if(lcm1>m){
            continue;
        }
        lcm1=lcm(lcm1,a[i]/2);
    }
    if(lcm1>m){cout<<0<<'\n';return 0;}
    int flag=0;
    for(int i=1;i<=n;i++){
        int temp=lcm1*2/a[i];
        if(temp%2==0){
            flag=1;
            break;
        }
    }
    if(flag){
        puts("0");
        return 0;
    }
    int cnt=m/lcm1;
    if(cnt&1){
        cnt=cnt/2+1;
    }
    else{
        cnt=cnt/2;
    }
    printf("%lld\n",cnt);
    return 0;
}