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: Runtime Error)

#include "bits/stdc++.h"

using namespace std;

int lcm(int a, int b){
    int x;
    x = a*b;
    if(a<b){
        swap(a,b);
    }
    int r = a%b;
    while(r !=0){
        a = b;
        b = r;
        r = a%b;
    }
    return x/b;
}
int main(){
    int n,m,x;
    cin >> n >> m;
    vector<int> a;
    while(n--) {
		cin >> x;
		a.push_back(x);
	}
    n = a.size();
    int p,q;
    p = a[0]/2;
    for(int i=0;i<n-1;i++){
        q = a[i+1]/2;
        p = lcm(p,q);
    }
    int ans;
    if(m < p){
        ans = 0;
    }else{
        ans = (m - p)/(2 * p) + 1;
    }
    cout << ans<<endl;
}