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 <iostream>
#include <vector>
#include <numeric>

using namespace std;

int lcm(int a, int b);
int gcd(int a, int b);

int main()
{
	long long n, m;
	cin >> n >> m;

	vector<long long> a(n);
	int max = 0;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	
	for (int i = n - 2; i >= 0; i--) {
		a[i] = lcm(a[i], a[i + 1]);
	}
	
	if (m < a[0]) {
		cout << 0 << endl;
	}
	else {
		cout << m / a[0] + 1 << endl;
	}

	return 0;
}

int gcd(int a, int b) 
{
	if (a < b)swap(a, b);
	while (b) {
		int r = a % b; a = b; b = r;
	}
	return a;
}

int lcm(int a, int b) 
{
	return (a * b / gcd(a, b));
}