## USACO 2021 US Open, Silver

## Problem 3. Acowdemia

Contest has ended.

**Log in to allow submissions in analysis mode**

Bessie has heard that an academic's success can be measured by their $h$-index. The $h$-index is the largest number $h$ such that the researcher has at least $h$ papers each with at least $h$ citations. For example, a researcher with $4$ papers and respective citation counts $(1,100,2,3)$ has an $h$-index of $2$, whereas if the citation counts were $(1,100,3,3)$ then the $h$-index would be $3$.

To up her $h$-index, Bessie is planning to write up to $K$ survey articles ($0 \leq K \leq 10^5$), each citing many of her past papers. However, due to page limits, she can only cite at most $L$ papers in each survey ($0 \leq L \leq 10^5$). Of course, no paper may be cited multiple times in a single survey (but a paper may be cited in several surveys).

Help Bessie determine the maximum $h$-index she may achieve after writing these survey articles. Bessie is not allowed to cite a survey from one of her surveys.

Note that Bessie's research advisor should probably inform her at some point that writing a survey solely to increase one's $h$ index is ethically dubious; other academics are not recommended to follow Bessie's example here.

#### INPUT FORMAT (input arrives from the terminal / stdin):

The first line contains $N$, $K$, and $L$.The second line contains $N$ space-separated integers $c_1,\ldots, c_N$.

#### OUTPUT FORMAT (print output to the terminal / stdout):

The maximum $h$-index on a single line.#### SAMPLE INPUT:

4 4 1 1 100 1 1

#### SAMPLE OUTPUT:

3

In this example, Bessie may write up to $4$ survey articles, each citing at most $1$ paper. If she cites each of her first and third articles twice, then her $h$-index becomes $3$.

#### SAMPLE INPUT:

4 1 4 1 100 1 1

#### SAMPLE OUTPUT:

2

In this second example, Bessie may write at most a single article. If Bessie cites any of her first, third, or fourth papers at least once, her $h$-index becomes $2$.

#### SCORING:

- Test cases 1-6 satisfy $N\le 100$.
- Test cases 7-16 satisfy no additional constraints.

Problem credits: Dhruv Rohatgi