A12410. Wrong Answer

Consider the following problem: given an array $a$ containing $n$ integers (indexed from $0$ to $n-1$ ), find $\max\limits_{0 \leq l \leq r \leq n-1} \sum\limits_{l \leq i \leq r} (r-l+1) \cdot a_i$ . In this problem, $1 \leq n \leq 2\,000$ and $|a_i| \leq 10^6$ .

In an attempt to solve the problem described, Alice quickly came up with a blazing-fast greedy algorithm and coded it. Her implementation in pseudocode is as follows:

```
<br></br><span class="tex-font-style-bf">function</span> find_answer(n, a)<br></br> # Assumes n is an integer between 1 and 2000, inclusive<br></br> # Assumes a is a list containing n integers: a[0], a[1], ..., a[n-1]<br></br> res = 0<br></br> cur = 0<br></br> k = -1<br></br><span class="tex-font-style-bf">for</span> i = 0 <span class="tex-font-style-bf">to</span> i = n-1<br></br> cur = cur + a[i]<br></br><span class="tex-font-style-bf">if</span> cur < 0<br></br> cur = 0<br></br> k = i<br></br> res = max(res, (i-k)*cur)<br></br><span class="tex-font-style-bf">return</span> res<br></br><br></br>
```

Also, as you can see, Alice's idea is not entirely correct. For example, suppose $n = 4$ and $a = [6, -8, 7, -42]$ . Then, find\_answer(n, a) would return $7$ , but the correct answer is $3 \cdot (6-8+7) = 15$ .

You told Alice that her solution is incorrect, but she did not believe what you said.

Given an integer $k$ , you are to find any sequence $a$ of $n$ integers such that the correct answer and the answer produced by Alice's algorithm differ by exactly $k$ . Note that although the choice of $n$ and the content of the sequence is yours, you must still follow the constraints earlier given: that $1 \leq n \leq 2\,000$ and that the absolute value of each element does not exceed $10^6$ . If there is no such sequence, determine so.

The first and only line contains one integer $k$ ( $1 \leq k \leq 10^9$ ).

If there is no sought sequence, print "-1".

Otherwise, in the first line, print one integer $n$ ( $1 \leq n \leq 2\,000$ ), denoting the number of elements in the sequence.

Then, in the second line, print $n$ space-separated integers: $a_0, a_1, \ldots, a_{n-1}$ ( $|a_i| \leq 10^6$ ).

The first sample corresponds to the example given in the problem statement.

In the second sample, one answer is $n = 7$ with $a = [30, -12, -99, 123, -2, 245, -300]$ , in which case find\_answer(n, a) returns $1098$ , while the correct answer is $1710$ .