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: Runtime Error)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
	"strings"
)

func solution(n, k int, nums []int) int {
	l := (n * (n - 1)) / 2

	var stack = make([][]int, 3)
	for i := range nums {
		switch {
		case nums[i] < 0:
			stack[0] = append(stack[0], nums[i])
		case nums[i] == 0:
			stack[1] = append(stack[1], nums[i])
		case nums[i] > 0:
			stack[2] = append(stack[2], nums[i])
		}
	}
	nn := len(stack[0])
	pn := len(stack[2])
	nns := pn * nn
	pns := (pn*(pn-1))/2 + (nn*(nn-1))/2
	zns := l - (nns + pns)

	var ans int
	switch {
	case k <= nns:
		memo := make([]int, nns)
		for _, n := range stack[0] {
			for _, p := range stack[2] {
				memo = append(memo, n*p)
			}
		}
		sort.Ints(memo)
		ans = memo[k-1]

	case k > nns && k <= nns+zns:
		ans = 0
	case k > nns+zns:
		memo := make([]int, 0, pns)
		for i := 0; i < nn; i++ {
			for j := i + 1; j < nn; j++ {
				memo = append(memo, stack[0][i]*stack[0][j])
			}
		}
		for i := 0; i < pn; i++ {
			for j := i + 1; j < pn; j++ {
				memo = append(memo, stack[2][i]*stack[2][j])
			}
		}
		sort.Ints(memo)
		ans = memo[k-1-(nns+zns)]
	}
	return ans
}

func main() {
	var n, k int
	fmt.Scan(&n, &k)

	reader := bufio.NewReaderSize(os.Stdin, 2*1e6)
	str, _, _ := reader.ReadLine()
	nums := make([]int, n)
	for i, s := range strings.Split(string(str), " ") {
		nums[i], _ = strconv.Atoi(s)
	}

	fmt.Println(solution(n, k, nums))
}