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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

MOD = 10**9 + 7
def main():
    n, k = map(int, input().split())# 正0でコーナー
    a = list(map(int, input().split()))
    pos = []
    neg = []
    zero = []
    for v in a:
        if v == 0:
            zero.append(v)
        elif 0 < v:
            pos.append(v)
        else:
            neg.append(v)
    if len(pos) + len(neg) < k:
        print(0)
    else:
        if k%2 == 0:
            if len(pos) + len(neg) == k and len(pos) % 2 == 1:#負になる
                if len(zero) > 0:
                    print(0)
                else:
                    ans = 1
                    for v in pos:
                        ans *= v
                        ans %= MOD
                    for v in neg:
                        ans *= v
                        ans %= MOD
                    print(ans % MOD)
            else:
                pos.sort(reverse=True)
                neg.sort()
                for i in range(1, len(pos)):
                    pos[i] *= pos[i-1]
                for i in range(1, len(neg)):
                    neg[i] *= neg[i-1]
                ans = 0
                for i in range(0, k+1, 2):
                    if len(pos) < i or len(neg) < k-i:
                        continue
                    tmp = 1
                    if 0 < i:
                        tmp *= pos[i-1]
                    if 0 < k-i:
                        tmp *= neg[k-i-1]
                    if ans < tmp:
                        ans = tmp
                print(ans % MOD)
        else:
            if 0 == len(pos):
                if 0 < len(zero):
                    print(0)
                else:
                    neg.sort(reverse=True)
                    ans = 1
                    for i in range(k):
                        ans *= neg[i]
                        ans %= MOD
                    print(ans)
            else:
                pos.sort(reverse=True)
                neg.sort()
                for i in range(1, len(pos)):
                    pos[i] *= pos[i-1]
                for i in range(1, len(neg)):
                    neg[i] *= neg[i-1]
                ans = 0
                for i in range(1, k+1, 2):
                    if len(pos) < i or len(neg) < k-i:
                        continue
                    tmp = 1
                    if 0 < i:
                        tmp *= pos[i-1]
                    if 0 < k-i:
                        tmp *= neg[k-i-1]
                    if ans < tmp:
                        ans = tmp
                print(ans % MOD)

if __name__ == "__main__":
    main()