#include <stdio.h>
#include <algorithm>
long long p = 1000000000;
long long l, r, m, t, k;
long long n, x, y, z, w;
long long a[200000];
int main() {
	l = p * p * (-1);
	r = p * p + 1;
	scanf("%lld%lld", &n, &k);
	for (int i = 0; i < n; i++) {
		scanf("%lld", a + i);
		if (a[i] < 0)x++;
		if (a[i] == 0)y++;
		if (a[i] > 0)z++;
	}
	std::sort(a, a + n);
	while (r - l > 1) {
		m = (r + l) / 2;
		t = 0;
		if (m == 0) {
			t = x * z;
		}
		if (m > 0) {
			t = x * z + (x + z) * y + y * (y - 1) / 2;
			w = n - 1;
			for (long long i = x + y; i < n; i++) {
				while (a[w] * a[i] >= m)w--;
				if (w > i)t += w - i;
				else break;
			}
			w = 0;
			for (long long i = x - 1; i >= 0; i--) {
				while (a[w] * a[i] >= m)w++;
				if (w < i)t += i - w;
				else break;
			}
		}
		if (m < 0) {
			w = x - 1;
			for (long long i = n - 1; i >= x + y; i--) {
				while (w >= 0 && a[w] * a[i] >= m)w--;
				if (w >= 0)t += w + 1;
			}
		}
		if (t < k)l = m;
		else r = m;
	}
	printf("%lld\n", l);
}

### Prompt

Please formulate a Cpp solution to 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 <stdio.h>
#include <algorithm>
long long p = 1000000000;
long long l, r, m, t, k;
long long n, x, y, z, w;
long long a[200000];
int main() {
	l = p * p * (-1);
	r = p * p + 1;
	scanf("%lld%lld", &n, &k);
	for (int i = 0; i < n; i++) {
		scanf("%lld", a + i);
		if (a[i] < 0)x++;
		if (a[i] == 0)y++;
		if (a[i] > 0)z++;
	}
	std::sort(a, a + n);
	while (r - l > 1) {
		m = (r + l) / 2;
		t = 0;
		if (m == 0) {
			t = x * z;
		}
		if (m > 0) {
			t = x * z + (x + z) * y + y * (y - 1) / 2;
			w = n - 1;
			for (long long i = x + y; i < n; i++) {
				while (a[w] * a[i] >= m)w--;
				if (w > i)t += w - i;
				else break;
			}
			w = 0;
			for (long long i = x - 1; i >= 0; i--) {
				while (a[w] * a[i] >= m)w++;
				if (w < i)t += i - w;
				else break;
			}
		}
		if (m < 0) {
			w = x - 1;
			for (long long i = n - 1; i >= x + y; i--) {
				while (w >= 0 && a[w] * a[i] >= m)w--;
				if (w >= 0)t += w + 1;
			}
		}
		if (t < k)l = m;
		else r = m;
	}
	printf("%lld\n", l);
}

```