Sliding Log Rate Limiter Admission Count

A sliding-window-LOG rate limiter admits at most m requests within any trailing window of w milliseconds. You are given n requests' arrival timestamps (integers, milliseconds since start, given in non-decreasing order). Process requests one at a time, in the given order. For a request with timestamp t:

• Its window is the half-open interval (t - w, t] - that is, ADMITTED requests with timestamp strictly greater than t - w and less than or equal to t.
• The request is ADMITTED if the number of PREVIOUSLY ADMITTED requests whose timestamp falls in that window is strictly less than m; otherwise it is REJECTED.
• Only ADMITTED requests are ever added to the log used for future window checks - rejected requests are discarded and never counted again.

Print the total number of ADMITTED requests.

Input format

Line 1: three integers n, w, m. Line 2: n space-separated non-decreasing integers, the request timestamps.

Output format

A single integer: the total number of admitted requests.

Constraints

• 1 <= n <= 100000
• 1 <= w <= 1000000
• 1 <= m <= 100000
• 0 <= timestamp <= 10000000, non-decreasing