D - Pairs

Score: $400$ points

Problem Statement

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.

4 3
3 3 -4 -2

-6

There are six ways to form a pair. The products of those pairs are $9$, $-12$, $-6$, $-12$, $-6$, $8$.

Sorting those numbers in ascending order, we have $-12$, $-12$, $-6$, $-6$, $8$, $9$. The third number in this list is $-6$.

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

6

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

448283280358331064