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 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>
typedef long long ll;
#define WA 1000000007
int gcd(int a,int b)
{
    if (a%b==0)
    {
        return(b);
    }
    else
    {
        return(gcd(b,a%b));
    }
}

int main()
{
    int n;
    ll m,ans=0;
    scanf("%d %lld",&n,&m);
    ll a[n];
    scanf("%lld",&a[0]);
    ll g=a[0],x;
    
    for(int i=1;i<n;i++){
        scanf("%lld",&a[i]);
        x = g*a[i];
        g = gcd(g,a[i]);
        g = x/g;
    }
    
    g/=2;
    m/=g;
    printf("%lld",(m+1)/2);
    
    
}