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 <stdio.h>
long long int gcd(long long int a, long long int b){return (a % b) ? gcd(b, a % b): b;}

int main(void){
    long long int a[100000];
    long long int n, m;
    scanf("%lld%lld", &n, &m);

    int i, j, k;
    
    for(i = 0; i < n; i++){
        scanf("%lld", &a[i]);
    }
    long long int tmp, lcm;
    tmp = a[0]/2;
    for(i = 1; i < n; i++){
        lcm = tmp*a[i]/2/gcd(tmp, a[i]/2);
    }
    long long int ans = (m/lcm + 1)/2;
    
    printf("%lld\n", ans);
}