Find Minimum Days

Each day, choose exactly k consecutive chapters and read at most p pages of each chosen chapter (a chapter with fewer than p pages left is simply finished). Chapters may be chosen repeatedly, and a finished chapter can still be chosen. Find the minimum number of days needed to finish every chapter.

输入格式

The first line contains n k p; the second line contains the page count of each chapter. 1≤n≤100000, 1≤k≤n, 1≤p,pages≤10^9.

输出格式

Output a single integer, the answer.

样例 1

输入：

3 2 2
3 1 4

输出：

4

样例 2

输入：

2 1 2
3 4

输出：

4

样例 3

输入：

3 3 10
1 1 1

输出：

1

样例说明

Example 1: choose the first two chapters twice and the last two chapters twice, 4 days in total. Example 2: each of the two chapters needs 2 days and they cannot be read on the same day, so the answer is 4. Example 3: one selection covers everything and p is large enough, so the answer is 1.