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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

MOD=1000000007
n,k=map(int,input().split())
a=[int(i) for i in input().split()]
pos=[]
neg=[]
nzero=0
for i in a:
    if i>0:
        pos.append(i)
    elif i<0:
        neg.append(-i)
    else:
        nzero+=1
if nzero+k>n:
    print(0)
elif nzero+k==n:
    if len(neg)%2:
        print(0)
    else:
        res=1
        for i in pos+neg:
            res*=i
            res%=MOD
        print(res)
elif len(pos)==0:
    res=1
    if k%2 and nzero>0:
        print(0)
    elif k%2:
        neg.sort()
        for i in range(k):
            res*=MOD-neg[i]
            res%=MOD
    else:
        neg.sort(reverse=True)
        for i in range(k):
            res*=MOD-neg[i]
            res%=MOD
    print(res)
elif len(neg)==0:
    res=1
    pos.sort(reverse=True)
    for i in range(k):
        res*=pos[i]
        res%=MOD
    print(res)
else:
    pos.sort(reverse=True)
    neg.sort(reverse=True)
    ruip=[1 for i in range(len(pos)+1)]
    ruin=[1 for i in range(len(neg)+1)]
    for i in range(len(pos)):
        ruip[i+1]=ruip[i]*pos[i]
        ruip[i+1]%=MOD
    for i in range(len(neg)):
        ruin[i+1]=ruin[i]*neg[i]
        ruin[i+1]%=MOD
    np=0
    if len(pos)>=k:
        np=k
    elif (k-len(pos))%2:
        np=len(pos)-1
    else:
        np=len(pos)
    while np>=2 and (pos[np-1]*pos[np-2]<neg[k-np-1]*neg[k-np-2]):
        np-=2
        if np+len(neg)<k:
            np+=2
            break
    print((ruip[np]*ruin[k-np])%MOD)