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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#pragma GCC optimize("O2")
#define rep(i,N) for(int i=0;i<(int)N;i++)
using namespace std;
const int MOD=1e9+7;

int main()
{
  int A[200000],N,K,l,m=0,r,accum=1,sign=1;long x,y;
  cin>>N>>K;
  rep(i,N)cin>>A[i],m+=A[i]<0?1:0;
  sort(A,A+N);
  if(K&1)accum=A[N-1],sign=(A[N-1]<0?-1:1),N--,K--;
  l=0,r=N-1;
  while(K)
  {
    x=1l*A[l]*A[l+1],y=1l*A[r]*A[r-1];
    if(x*sign>y*sign)x%=MOD,accum=1l*accum*x%MOD,l+=2;
    else y%=MOD,accum=1l*accum*y%MOD,r-=2;
    K-=2;
  }
  return printf("%ld\n",(1l*accum%MOD+MOD)%MOD),0;
}