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 main() {

	var Nstr string
	sc1 := bufio.NewScanner(os.Stdin)

	if sc1.Scan() {
		Nstr = sc1.Text()
	}

	N, _ := strconv.Atoi(strings.Split(Nstr, " ")[0])
	K, _ := strconv.Atoi(strings.Split(Nstr, " ")[1])

	var cardStr string
	sc := bufio.NewScanner(os.Stdin)
	if sc.Scan() {
		cardStr = sc.Text()
	}

	Ntotal := N * (N - 1) / 2
	var tmpInt []int
	tmpInt = make([]int, N, N)

	var total []int
	total = make([]int, Ntotal, Ntotal)

	cardArray := strings.Split(cardStr, " ")

	for i, valueStr := range cardArray {
		value, _ := strconv.Atoi(valueStr)
		tmpInt[i] = value
	}

	var cnt int
	for i := 0; i < N; i++ {
		for j := i + 1; j < N; j++ {
			total[cnt] = tmpInt[i] * tmpInt[j]
			cnt++
		}
	}

	sort.Sort(sort.IntSlice(total))

	fmt.Println(total[K-1])

}