Acowdemia#11236
Bessie has published papers. The -th paper has accumulated c_i citations.
The -index is the largest number such that the researcher has at least papers each with at least citations. For example, a researcher with papers and respective citation counts (1, 100, 2, 3) has an -index of , whereas if the citation counts were (1, 100, 3, 3) then the -index would be .
To up her -index, Bessie is planning to write up to survey articles, each citing many of her past papers. However, due to page limits, she can only cite at most papers in each survey. 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 -index she may achieve after writing these survey articles. Bessie is not allowed to cite a survey from one of her surveys.
The first line contains (1 \le n \le 10^5), (0 \le k \le 10^5) and (0 \le l \le 10^5).
The second line contains integers c_1, \ldots, c_n (0 \le c_i \le 10^5).
Print the maximum -index on a single line.
Example 1
Example 2
Example 1
In this example, Bessie may write up to survey articles, each citing at most paper. If she cites each of her first and third articles twice, then her -index becomes .
Example 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 -index becomes .