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)

'use strict'

function Main(input) {
  input = input.trim().split('\n')
  const A = input[1].split(' ').map(s => parseInt(s))
  const res = input[0].split(' ').map(s => parseInt(s))
  const N = res[0]
  const K = res[1]

  let results = []
  for(let i = 0; i < N - 1; ++i) {
    const a = A[i]
    for (let j = i + 1; j < N; ++j) {
      const b = A[j]
      results.push(a * b)
    }
  }

  results = results.sort((a, b) => a - b)
  console.log(results[K - 1])
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));