Multiplication 4

AtCoder

IDabc173_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $K$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

4 2
1 2 -3 -4

Output #1

12

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

Input #2

4 3
-1 -2 -3 -4

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, $1000000001$.

Input #3

2 1
-1 1000000000

Output #3

1000000000

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

Input #4

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

Output #4

999983200

Be sure to print the product modulo $(10^9+7)$.

API Response (JSON)

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      "statement_type": "Markdown",
      "content": "Given are $N$ integers $A_1,\\ldots,A_N$.\nWe will choose exactly $K$ of these elements. Find the maximum possible product of the chosen elements.\nThen, print the maximum product modulo $(10^9+7)$, usin...",
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