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: Accepted)

n, k = map(int, input().split())
al = list(map(int, input().split()))
al_abs = []
al_p = []
al_m = []
zero_cnt = 0
MOD = 10**9+7

if n == 1 and k == 1:
    print(al[0]%MOD)
    exit()

if n == k:
    ans = 1
    for a in al:
        ans *= a
        ans %= MOD
    print(ans)
    exit()

for a in al:
    if a == 0:
        zero_cnt+=1
    else:
        if a > 0: 
            al_abs.append((abs(a),1))
            al_p.append(a)
        elif a < 0: 
            al_abs.append((abs(a),-1))

al_abs.sort(reverse=True)
if len(al_abs) < k:
    print(0)
    exit()

if len(al_abs) == k:
    ans = 1
    m_cnt = 0
    for a,s in al_abs:
        if s == -1: m_cnt += 1
        ans *= a
        ans %= MOD
    if m_cnt%2 == 0:
        print(ans)
    else:
        print(0)
    exit()
    

if not al_p:
    if k%2 == 1 and zero_cnt > 0:
        print(0)
    else:
        if k%2 == 1:
            al_abs.sort()
        ans = 1
        for a,s in al_abs[:k]:
            ans *= (a*(-1))
            ans %= MOD
        print(ans)
    exit()



val = 1
m_cnt = 0
last_m = 0
last_p = 0
for i in range(k):
    v,sig = al_abs[i]
    val *= v
    val %= MOD
    if sig == -1:
        m_cnt += 1
        last_m = v
    else:
        last_p = v

if m_cnt %2 == 0:
    print(val)
    exit()


# minus -> plus 

## search next p
next_p = 0
for i in range(k,len(al_abs)):
    v,sig = al_abs[i]
    if sig == 1:
        next_p = v
        break

## search next m
next_m = 0
for i in range(k,len(al_abs)):
    v,sig = al_abs[i]
    if sig == -1:
        next_m = v
        break

# print(next_m, next_p)

if next_p == 0 and next_m == 0:
    print(0)
    exit()

# last_m -> next_p
if next_p*last_p >= next_m*last_m or last_p == 0:
# if next_p > 0 and next_m == 0:
    ans = 1
    skip_flag = False
    for i in range(k):
        v,sig = al_abs[i]
        if not skip_flag and v == last_m and sig == -1:
            ans *= next_p
            skip_flag = True
        else:
            ans *= v
        # print(ans)
        ans %= MOD
    print(ans)
    exit()


# last_p -> next_m
# if next_p == 0 and next_m > 0:
elif next_p*last_p <= next_m*last_m:
    ans = 1
    skip_flag = False
    for i in range(k):
        v,sig = al_abs[i]
        if not skip_flag and v == last_p and sig == 1:
            ans *= next_m
            skip_flag = True
        else:
            ans *= v
        ans %= MOD
    print(ans)
    exit()