#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
inline LL read() {
	LL x = 0, fh = 1;
	char c = getchar();
	while (c < '0' || c > '9') {
		if (c == '-') fh = -1;
		c = getchar();
	}
	while (c >= '0' && c <= '9') {
		x = (x << 1) + (x << 3) + c - '0';
		c = getchar();
	}
	return x * fh;
}
const LL N = 2e5 + 10, INF = 1e18;
LL n, k, l, r, mid, ll, rr, mmid, cnt, i, a[N];
int main() {
	n = read(); k = read();
	for (i = 0; i < n; i++) a[i] = read();
	sort(a, a + n);
	l = -INF; r = INF;
	while (l + 1 < r) {
		mid = l + r >> 1;
		cnt = 0;
		for (i = 0; i < n; i++) {
			if (a[i] < 0) {
				ll = i; rr = n;
				while (ll + 1 < rr) {
					mmid = ll + rr >> 1;
					if (a[i] * a[mmid] <= mid) rr = mmid;
					else ll = mmid;	
				}
				cnt += n - rr;
			}
			else {
				ll = i; rr = n;
				while (ll + 1 < rr) {
					mmid = ll + rr >> 1;
					if (a[i] * a[mmid] <= mid) ll = mmid;
					else rr = mmid;
				}
				cnt += ll - i;
			}
		} 
		if (cnt < k) l = mid;
		else r = mid;
	}
	cout << r;
	return 0;
}
### Prompt

Your task is to create 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 <bits/stdc++.h>
using namespace std;
typedef long long LL;
inline LL read() {
	LL x = 0, fh = 1;
	char c = getchar();
	while (c < '0' || c > '9') {
		if (c == '-') fh = -1;
		c = getchar();
	}
	while (c >= '0' && c <= '9') {
		x = (x << 1) + (x << 3) + c - '0';
		c = getchar();
	}
	return x * fh;
}
const LL N = 2e5 + 10, INF = 1e18;
LL n, k, l, r, mid, ll, rr, mmid, cnt, i, a[N];
int main() {
	n = read(); k = read();
	for (i = 0; i < n; i++) a[i] = read();
	sort(a, a + n);
	l = -INF; r = INF;
	while (l + 1 < r) {
		mid = l + r >> 1;
		cnt = 0;
		for (i = 0; i < n; i++) {
			if (a[i] < 0) {
				ll = i; rr = n;
				while (ll + 1 < rr) {
					mmid = ll + rr >> 1;
					if (a[i] * a[mmid] <= mid) rr = mmid;
					else ll = mmid;	
				}
				cnt += n - rr;
			}
			else {
				ll = i; rr = n;
				while (ll + 1 < rr) {
					mmid = ll + rr >> 1;
					if (a[i] * a[mmid] <= mid) ll = mmid;
					else rr = mmid;
				}
				cnt += ll - i;
			}
		} 
		if (cnt < k) l = mid;
		else r = mid;
	}
	cout << r;
	return 0;
}
```