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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program abc5
 implicit none
 integer::N=0,K=0,s=0,i,ishota,ishotb,p=0,q=0
 integer,allocatable::a(:)
 read(*,*)N,K
 allocate(a(N))
 read(*,*)(a(i),i=1,N)
 do ishota=1,N
  do ishotb=1,N-1
   if(a(ishotb)>a(ishotb+1))then
    p=a(ishotb)
    q=a(ishotb+1)
    a(ishotb)=q
    a(ishotb+1)=p
   end if
  end do
 end do
 s=product(a(N-K+1:N))
 print'(i0)',mod(s,(10**9+7))
 deallocate(a)
end program abc5