Problem7024--ABC173 —— E - Multiplication 4

7024: ABC173 —— E - Multiplication 4

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Time Limit : 1.000 sec  Memory Limit : 256 MiB

Description

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).

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).

Constraints

$1≤K≤N≤2×10^5$
$|A_i| \leq 10^9$

Sample 1 Input

4 2
1 2 -3 -4

Sample 1 Output

12
The possible products of the two chosen elements are $2, -3, -4, -6, -8$, and $12$, so the maximum product is $12$.

Sample 2 Input

4 3
-1 -2 -3 -4

Sample 2 Output

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 3 Input

2 1
-1 1000000000

Sample 3 Output

1000000000
The possible products of the one chosen element are $-1$ and $1000000000$, so the maximum product is $1000000000$.

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1

999983200

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