Preparation#775
Vasya decided to thoroughly prepare for the second round of the Olympiad in Informatics. To do this, he wants to organize small Olympiads for himself, each consisting of problems. In order to come up with problems for these Olympiads, Vasya needs collections of Olympiad problems. These collections are available in the library. It is known that there are exactly collections in the library, and the -th collection contains exactly a_i problems.
Vasya does not want to go to the library many times; he wants to take, in one visit, enough collections to prepare all Olympiads. What is the minimum number of collections he must take from the library?
The first line contains three natural numbers , , — the number of collections in the library, the number of problems in one Olympiad, and the number of Olympiads (1 \le k \le 100\,000, 1 \le m, n \le 10\,000). The second line contains natural numbers: a_1,\ a_2,\ \ldots,\ a_k. Here, a_i (1 \le a_i \le 10^9) is the number of problems in the -th collection.
Print the minimum number of collections that Vasya needs to take from the library. You may assume that the library contains enough collections for Vasya to prepare the Olympiad problems.
Example 1