Besi has published
N articles (1 <= N <= 10
5).
ith article cited
ci times (0 <= c
i <=
;10
5).
h-index is the largest number of
h such that there are at least
h articles, each of which is cited by at least
h code> times. For example, there are 4 articles with the number of citations (1,100,2,3), then the
h-index is 2, and with the number of citations (1,100,3,3)
h- index is 3.
To increase her
h-index, Besi plans to write
K review articles (0 <= K <= 10
5), each of which cites several of her past articles. Besi has the right to cite no more than
L articles in each review (0 <= L <= 10
5). Of course, no article can be cited more than once in one review (however, an article can be cited in several reviews).
Help Besi determine the maximum
h-index she can reach after writing these review articles. Besi cannot quote a review in any of her reviews.
Input data
The first line contains
N, K, L. The second line contains
N space-separated integers
c1,
...,
cN.
Imprint
Maximum
h-index.
Examples
| # |
Input |
Output |
Explanation |
| 1 |
4 4 1
1 100 1 1
| 3 |
In this example, Besi can write 4 review articles, each of which can cite no more than 1 article. If you quote the first and third articles 2 times, its h-index becomes 3. |
| 2 |
4 1 4
1 100 1 1
| 2 |
In this second example, Besi can write at most one article. If Besi cites any of her 1st, 2nd or 4th articles at least once, her h-index will become 2. |