Problem:
Score : 500 points

Problem Statement

Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

1 \leq K \leq N \leq 2\times 10^5

|A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:

N K
A_1 \ldots A_N

Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Sample Input 1

4 2
1 2 -3 -4

Sample Output 1

12

The possible products of the two chosen elements are 2, -3, -4, -6, -8, and 12, so the maximum product is 12.

Sample Input 2

4 3
-1 -2 -3 -4

Sample Output 2

1000000001

The possible products of the three chosen elements are -24, -12, -8, and -6, so the maximum product is -6.

We print this value modulo (10^9+7), that is, 1000000001.

Sample Input 3

2 1
-1 1000000000

Sample Output 3

1000000000

The possible products of the one chosen element are -1 and 1000000000, so the maximum product is 1000000000.

Sample Input 4

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

Sample Output 4

999983200

Be sure to print the product modulo (10^9+7).

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

const [nk, as] = require('fs').readFileSync('/dev/stdin', 'utf8').split(/\n/)
const [n, k] = nk.split(/\s/).map(Number)
const arr = as.split(/\s/).map(Number).sort((a, b) => Math.abs(b) - Math.abs(a))
const base = Math.pow(10, 9) + 7

let results = [], lowestP = -1, lowestN = -1, odd = false

for (let i = 0; i < k; i++) {
  results.push(arr[i])
  if (arr[i] < 0) {
    lowestN = i
    odd = !odd
  } else {
    lowestP = i
  }
}
if (odd) {
  let mul1 = lowestP >= 0 ? 1 / results[lowestP] : 0
  let mul2 = lowestN >= 0 ? 1 / -results[lowestN] : 0
  let index1 = -1
  let index2 = -1
  for (let i = k; i < n; i++) {
    if (arr[i] < 0 && index1 < 0) {
      mul1 *= -arr[i]
      index1 = i
    } else if (arr[i] > 0 && index2 < 0) {
      mul2 *= arr[i]
      index2 = i
    }
    if ((index1 >= 0 || mul1 === 0) && (index2 >= 0 || mul2 === 0)) {
      break
    }
  }
  const v1 = mul1 * Number(index1 >= 0), v2 = mul2 * Number(index2 >= 0)
  if (!v1 && !v2) {
    results = []
  } else if (v1 > v2) {
    results[lowestP] = arr[index1]
  } else {
    results[lowestN] = arr[index2]
  }
}
if (results.length === 0) {
  let result = 1;
  for (let i = n - 1; i >= n - k; i--) {
    result = (result * arr[i]) % base
  }
  console.log(result + base)
} else {
  let result = 1;
  for (const r of results) {
    result = (result * r) % base
  }
  console.log(result)
}