P15532 【MYCOI R1】The Call of Love
Background
> If only I had the chance, I'd want to shout "I love you" so loudly!
>
> —— Xiao Che
Xiao Che and his classmates are preparing to perform the song "I Want to Shout 'I Love You'" in a choir competition. However, the teacher thinks they are all too short and has decided to ask you, the magician, to help them grow taller.
Description
There are $n$ children standing in a row. The height of the $i$-th child is $a_i$ centimeters.
As a magician, you have two types of magic:
- **"Lock"**: Point your wand at a child.
- **"Grow"**: Increase the height of the **last child whom your wand is pointing to by $1$ centimeter. **Note: If you have never performed "Lock" before, you cannot perform this magic.**
The teacher thinks that if only one child keeps growing taller, the neighboring children might feel inferior. Therefore, the teacher requires that you may only perform the **"Grow"** magic if, within the $L$ children to the left (or up to the start of the line if fewer than $L$ exist) and the $L$ children to the right (or up to the end of the line if fewer than $L$ exist) of the chosen child, there is **at least** one child whose height is greater than or equal to the chosen child's height.
Since magic requires casting time, the teacher wants to know the **minimum total number of magic actions (both "Grow" and "Lock")** required to make every child’s height **at least $M$**.
If it is impossible, output `Che_is_Loser`.
Input Format
The first line contains three positive integers $n$, $L$, $M$.
The second line contains $n$ positive integers $a_i$, separated by spaces.
A single positive integer representing the minimum number of operations required.
Output Format
A single positive integer representing the minimum number of operations required.
Explanation/Hint
**This problem uses bundled testing.**
::cute-table{tuack}
| Subtask | Special Properties | Points |
|:-------:|:-----------------:|:------:|
| Subtask 1 | $n, a_i, M, L \leq 10$ | 10 |
| Subtask 2 | $M \leq \min\{a_i\}$ | 1 |
| Subtask 3 | $M \leq \max\{a_i\}$ | 20 |
| Subtask 4 | $a_i$ is non-decreasing | 20 |
| Subtask 5 | No special properties | 49 |
For $100\%$ of the data, it is guaranteed that $2 \leq L \leq n \leq 10^6$, $1 \leq M, a_i \leq 10^9$.