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: Accepted)

console.log((args=>{
  const [[N,K],A] = args.trim().split('\n').map( r=>r.split(' ').map(v=>v|0) );
  const MOD = BigInt(1e9+7), mul = (a,b) => (BigInt(a)*BigInt(b)%MOD+MOD)%MOD;
  if ( K === N ) return `${A.reduce(mul,1)}`;
  let Am = [], Ap = [], zero = 0;
  for ( let i = 0; i < N; i++ ) {
    if ( A[i] > 0 ) Ap.push(A[i]);
    if ( A[i] < 0 ) Am.push(A[i]);
    if ( A[i] === 0 ) zero++;
  }
  if ( K+zero > N ) return '0';
  Am.sort((a,b)=>a-b);
  Ap.sort((a,b)=>b-a);
  if ( Ap.length === 0 && K&1 ) return zero?'0':`${ Am.slice(-K).reduce(mul,1) }`;
  let om = 0, op = 0, ap = [], am = [];
  for ( let i = 0; i < K; i++ ) {
    if ( (Ap[op]|0) > -(Am[om]|0) ) {
      ap.push(Ap[op]); op++;
    } else {
      am.push(Am[om]); om++;
    }
  }
  if ( am.length&1 ) {
    if ( am.length === Am.length 
      || BigInt(Ap[op]|0)*BigInt(Ap[op-1]|0) > BigInt(Am[om-1]|0)*BigInt(Am[om]|0)
      || am.length === K ) {
      am.pop();
      ap.push(Ap[op]);
    }
    else {
      ap.pop();
      am.push(Am[om]);
    }
  }
  return `${mul(ap.reduce(mul,1),am.reduce(mul,1))}`;
})(require('fs').readFileSync('/dev/stdin', 'utf8')));