A turnstile logs n entry events, each stamped with a time. Timestamps are given in non-decreasing order. For each event, report how many events (including this one) happened strictly within the last W time units - that is, how many logged events have a timestamp greater than (this event's timestamp) - W.
Because timestamps never decrease, this count is exactly the number of events whose timestamp t_j satisfies t_j > t_i - W, considering only events at or before the current one.
Input format
Line 1: two integers n and W.
Line 2: n space-separated integers, the timestamps in non-decreasing order.
Output format
One line with n space-separated integers: for each event (in order), the count of recent events as defined above.
Constraints
- 1 <= n <= 100000
- 1 <= W <= 1000000000
- 0 <= each timestamp <= 1000000000, given in non-decreasing order