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++ (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <boost/math/common_factor_rt.hpp>
using namespace std;
using uint = unsigned int;
using ull = unsigned long long;

int main() {
	uint N, M;
	cin >> N >> M;
	
	vector<uint> A(N);
	for(uint i=0; i<N; i++) {
		uint a;
		cin >> a;
		if(a % 2 == 1) {
			cout << 0;
			return 0;
		}
		A[i] = a / 2;
	}
	
	uint t = 1;
	uint a = A[0];
	while(a % 2 == 0) {
		t *= 2;
		a /= 2;
	}
	
	ull lcmA = 1;
	for(uint i=0; i<N; i++) {
		if(A[i] % t != 0) {
			cout << 0;
			return 0;
		} else {
			lcmA = boost::math::lcm(lcmA, ull(A[i] / t));
		}
	}
	
	ull ans = ((M / t / lcmA) + 1 )/ 2;

	cout << ans;
	return 0;
}