Laboratory work
Mikhail Vladimirovich, the strict professor at the Faculty of Applied Magic and Illusion at Byteland State University, has assigned his students a lab project involving problems across various topics. There are N topics in total, numbered from 1 to N, with A_i problems assigned to the i-th topic.
The students have decided to collaborate, as the problems are identical for everyone. Each ordinary student can solve one problem from any topic per day. Luckily, there's a 10th-grader named Gena among them, who attends classes out of interest. Gena can solve up to X problems per day, but due to the complexity of Mikhail Vladimirovich's problems, Gena cannot tackle problems from different topics on the same day.
Mikhail Vladimirovich has a total of K students. Your task is to help the students and Gena distribute the workload so that all problems are solved in the minimum number of days.
Input
The first line of input contains three integers N, X, and K, which represent the number of topics, the number of problems Gena can solve in one day, and the number of students, respectively (1 ≤ N ≤ 10^5, 0 ≤ X, K ≤ 10^9, 1 ≤ X+K).
The following N lines each contain an integer A_i, indicating the number of problems for the corresponding topic (1 ≤ A_i ≤ 10^9).
The number of problems for the topic numbered i is given on the (i+1)-th line.
Output
Output a single line with the minimum number of days required for the students and Gena to solve all the problems from the lab work.
Notes on examples
In the first example, Gena is equivalent to a regular student, solving one problem per day. With a total of 15 problems, the three students and Gena cannot complete them in less than four days.
In the second example, Gena can solve up to four problems per day. A possible plan to solve all the problems is as follows:
On the first day, Gena solves all the problems from the fourth topic, while the students solve two problems from the fifth topic.
On the second day, Gena solves the remaining four problems from the fifth topic, and the students solve two problems from the third topic.
On the third day, Gena solves all the problems from the second topic, and the students solve the remaining problems from the first and third topics.