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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <vector>

long long gcd(long long a, long long b) {
	return b == 0 ? a : gcd(b, a % b);
}

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

int main() {
	long long N, M;
	std::cin >> N >> M;
	std::vector<long long> a(N);
	for (int i = 0; i < N; i++) {
		std::cin >> a[i];
		a[i] /= 2;
	}
	long long l = a[0];
	for (int i = 1; i < N; i++) {
		l = lcm(a[i], l);
		if (l > M) {
			std::cout << 0 << std::endl;
			return 0;
		}
	}
	M += l;
	std::cout << M / (l * 2LL) << std::endl;

	return 0;
}