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 PyPy2 (7.3.0) (judge verdict: Runtime Error)

n,k=[int(i) for i in raw_input().split()]
a=[int(i) for i in raw_input().split()]
a.sort()
b=[]
c=[]
for i in range(n):
    if a[i]<0:
        b.append(a[i])
    else:
        c.append(a[i])
b.sort()
c.sort()
o=[]
i=0;n=len(c);m=len(b);l=0
j=n-1
if(k%2):
    o.append(c[j])
    j-=1
    l+=1
while l<k:
    if(j>0 and i<m-1 and l<k-1):
        if(c[j]*c[j-1])>(b[i])*(b[i+1]):
           o+=[c[j],c[j-1]]
           j-=2
        else:
           o+=[b[i],b[i+1]]
           i+=2
        l+=2
    elif(i<m-1 and l<k-1):
        o+=[b[i],b[i+1]]
        l+=2
        i+=2
    elif(j>-1):
        o+=[c[j]]
        l+=1
        j-=1
    
if n==0:
    o=b[m-k:]
s=1
for i in o:
    s*=i
    s%=(10**9+7)
print s