A single service counter opens at time 0 and serves customers strictly in the order they arrive (first-come-first-served), one at a time. You are given n customers' arrival times, given in non-decreasing order (since they form a single physical line), and a fixed service duration s: every customer takes exactly s minutes once their service begins.
Service of the next customer in line begins at max(arrival time, counter free time). A customer's wait time is (service start time - arrival time).
Count how many customers wait STRICTLY MORE than w minutes before being served.
Input format
Line 1: three integers n, s, w.
Line 2: n space-separated non-decreasing integers, the arrival times.
Output format
A single integer: the number of customers whose wait time is strictly greater than w.
Constraints
- 1 <= n <= 100000
- 1 <= s <= 1000
- 0 <= w <= 1000000
- 0 <= arrival time <= 1000000, non-decreasing