Hit Counter Over A Sliding Window

You are building a counter that reports how many events happened during the last W seconds.

The first line gives q and the window width W. Then q commands follow, each carrying a timestamp t. Timestamps across the whole command stream are non-decreasing (each command's t is greater than or equal to the previous command's t).

Support two commands:

• HIT t — record one hit that occurred at time t. Produces no output. (Multiple hits may share the same timestamp.)
• COUNT t — print how many recorded hits have a timestamp strictly greater than t - W and less than or equal to t; that is, hits lying in the half-open interval (t - W, t].

Input format

Line 1: two integers q and W. Each of the next q lines is HIT t or COUNT t.

Output format

For each COUNT command, print a single integer: the number of hits inside the window (t - W, t]. Print the answers in command order, one per line.

Constraints

• 1 ≤ q ≤ 100000
• 1 ≤ W ≤ 1000000000
• 1 ≤ t ≤ 1000000000
• Timestamps are non-decreasing across the command stream.