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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

// inputに入力データ全体が入る
function Main(input) {
	// 1行目がinput[0], 2行目がinput[1], …に入る
	var ans = 0
	input = input.trim().split("\n");
	s = input[1].split(' ').map((n) => (BigInt(n)))
	c = input[0].split(' ').map((n) => (n))[1]

	var arr = []
	for (var i = 0; i <= s.length; i++) {
		for (var j = i + 1; j < s.length; j++) {
		  arr.push(BigInt(s[i]) * BigInt(s[j]))	
		}
	}
	ans = arr.sort(function(a, b) { return BigInt(a) - BigInt(b)})
	var a = ans[c - 1]



	//出力
	console.log(BigInt(a).toString())
}
// *この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));
// Main(require('fs').readFileSync('./input.txt', 'utf-8'));