Problem:
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.

Sample Input 1

4 3
3 3 -4 -2

Sample Output 1

-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.

Sample Input 2

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

Sample Output 2

6

Sample Input 3

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

Sample Output 3

448283280358331064

Solution in Go (1.6) (judge verdict: Time Limit Exceeded)

package main
import (
  "fmt"
  "sort"
)
func main() {
  var n,k,x,y,z,c int
  fmt.Scan(&n,&k)
  a := make([]int,n)
  for i:=0;i<n;i++ { fmt.Scan(&a[i]) }
  sort.Ints(a)
  b := make([]int,n)
  for i:=0;i<n;i++ { b[i] = a[n-i-1] }
  x,z = -1e18,1e18
  for z-x > 1 {
    y = (x+z)/2
    c = 0
    for i:=0;i<n;i++ {
      t := a[i+1:]
      if a[i] < 0 { t = b[:n-i-1] }
      l,r := -1,len(t)
      for r-l > 1 {
        m := (l+r)/2
        if a[i]*t[m] < y { l = m } else { r = m }
      }
      c += r
    }
    if c < k { x = y } else { z = y }
  }
  fmt.Println(x)
}