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 <bits/stdc++.h>

using namespace std;
using llong = long long;
using ldbl = long double;
using lpair = pair<llong, llong>;

#define ALL(x) x.begin(), x.end()

template<typename T>
constexpr T inf = static_cast<T>(pow(10, static_cast<int>(log10(numeric_limits<T>::max())))) + 7;
constexpr llong mod = 1e9+7;

llong GCD(llong a, llong b){
	a = abs(a), b = abs(b);
	while(b){
		a %= b;
		swap(a,b);
	}

	return a;
}

llong LCM(llong a, llong b){
	return a / GCD(a, b) * b;
}

int main() {
	llong N, M;
	vector<llong> A;

	cin >> N >> M;
	A.resize(N);
	for (auto &in: A) {
		cin >> in;
		in /= 2;
	}

	llong l = A[0];
	for (auto a: A) {
		l = LCM(l, a);
		if (l > M) break;
	}

	if (l > M) {
		assert(false);
		cout << 0 << endl;
	}
	else {
		cout << M / l / 2 + (M % l > 0) << endl;
	}

	return 0;
}