#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const char sp = ' ';

int N;
ll K, A[200000], L, R;

int main() {
	cin >> N >> K;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
	}
	sort(A, A + N);
	L = -2e18;
	R = 2e18;
	while (L + 1 < R) {
		ll M = (L + R) / 2;
		ll cnt = 0;
		for (int i = 0; i < N; i++) {
			if (A[i] < 0) {
				int l, r;
				l = i;
				r = N;
				while (l + 1 < r) {
					int m = (l + r) / 2;
					if (A[i] * A[m] <= M) {
						r = m;
					}
					else {
						l = m;
					}
				}
				cnt += N - r;
			}
			else {
				int l, r;
				l = i;
				r = N;
				while (l + 1 < r) {
					int m = (l + r) / 2;
					if (A[i] * A[m] <= M) {
						l = m;
					}
					else {
						r = m;
					}
				}
				cnt += l - i;
			}
		}
		if (cnt < K)L = M;
		else R = M;
	}
	cout << R << endl;
}


### Prompt

In Cpp, your task is to solve the following problem:

We have N integers A_1, A_2, ..., A_N.

There are \frac{N(N-1)}{2} ways to choose two of them and form a pair. If we compute the product of each of those pairs and sort the results in ascending order, what will be the K-th number in that list?

Constraints

* All values in input are integers.
* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \frac{N(N-1)}{2}
* -10^9 \leq A_i \leq 10^9\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:


N K
A_1 A_2 \dots A_N


Output

Print the answer.

Examples

Input

4 3
3 3 -4 -2


Output

-6


Input

10 40
5 4 3 2 -1 0 0 0 0 0


Output

6


Input

30 413
-170202098 -268409015 537203564 983211703 21608710 -443999067 -937727165 -97596546 -372334013 398994917 -972141167 798607104 -949068442 -959948616 37909651 0 886627544 -20098238 0 -948955241 0 -214720580 277222296 -18897162 834475626 0 -425610555 110117526 663621752 0


Output

448283280358331064

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const char sp = ' ';

int N;
ll K, A[200000], L, R;

int main() {
	cin >> N >> K;
	for (int i = 0; i < N; i++) {
		cin >> A[i];
	}
	sort(A, A + N);
	L = -2e18;
	R = 2e18;
	while (L + 1 < R) {
		ll M = (L + R) / 2;
		ll cnt = 0;
		for (int i = 0; i < N; i++) {
			if (A[i] < 0) {
				int l, r;
				l = i;
				r = N;
				while (l + 1 < r) {
					int m = (l + r) / 2;
					if (A[i] * A[m] <= M) {
						r = m;
					}
					else {
						l = m;
					}
				}
				cnt += N - r;
			}
			else {
				int l, r;
				l = i;
				r = N;
				while (l + 1 < r) {
					int m = (l + r) / 2;
					if (A[i] * A[m] <= M) {
						l = m;
					}
					else {
						r = m;
					}
				}
				cnt += l - i;
			}
		}
		if (cnt < K)L = M;
		else R = M;
	}
	cout << R << endl;
}


```