Vasya decided to prepare for the second round of Olympiad in Informatics. So he decided to make for himself n small Olympiads, each with m tasks. In order to create tasks for these competitions, Vasya needs digests for Olympiad problems. These digests are located in the library. It is known that library contains exactly k digests. And i-th digest contains exactly ai tasks. Vasya do not want to go to the library many times, he wants at once to take the right amount of digests to create problems for all n competitions. What is the minimum number of digests he needs to take with him from the library?

Input

The first line contains three natural numbers k, m, n, where k is the number of digests in the library, m is the number of tasks in a single Olympiad, n is number of Olympiads (1 ≤ k ≤ 100 000, 1 ≤ m, n ≤ 10 000). The second line contains k integers a1, ..., ak. Here ai (1 ≤ ai ≤ 109) is a number of tasks in the i-th digest.

Output

Print the minimum number of digests that Vasya has to take from the library. We can assume that the library has sufficient number of digests for Vasya to finish his job.