Ants and Sugar Cubes Experiment

JOI is a biologist who performs experiments on ants and sugar cubes on a wooden stick of length (10^9). The stick is placed from left to right, and a point at distance (x) from the left end is referred to as the point with coordinate (x).

Initially, the stick is empty. JOI will perform (Q) operations. The (i)-th operation ((1 \le i \le Q)) is described by three integers (T_i, X_i, A_i):

• If \(T_i = 1\), then JOI places \(A_i\) ants at the point with coordinate \(X_i\).
• If \(T_i = 2\), then JOI places \(A_i\) sugar cubes at the point with coordinate \(X_i\).

Note that since both ants and sugar cubes are very small, they may be placed at the same point, and the same point might be used in multiple operations.

In this experiment, the ants have a cute trait of being very curious. Specifically, when JOI claps his hands, each ant will perform the following action:

• If there exists at least one sugar cube within a distance \(L\) (i.e. if there is a sugar cube at some coordinate \(y\) such that \(|X_{ant} - y| \le L\)), the ant will choose any one sugar cube and eat it.

Note that the same sugar cube may be eaten by more than one ant. For each \(k\) \((1 \le k \le Q)\), JOI wants to know:

• If he claps immediately after the \(k\)-th operation, what is the maximum number of sugar cubes that can be eaten by at least one ant?

It is important to note that JOI does not actually clap his hands – that is, the positions of the ants do not change and the sugar cubes are not actually removed.

Your task is to answer JOI's question for every prefix \(k\) (\(1 \le k \le Q\)).

inputFormat

The first line contains two integers (Q) and (L) ((1 \le Q \le \text{some upper limit},\ 0 \le L \le 10^9)).

Then (Q) lines follow. The (i)-th line contains three space-separated integers (T_i), (X_i), and (A_i). If (T_i = 1), it means an ant is placed at position (X_i); if (T_i = 2), it means sugar cubes are placed at position (X_i).

outputFormat

Output (Q) lines. The (k)-th line should contain the maximum number of sugar cubes that can be eaten by at least one ant, given that all operations from 1 to (k) have been performed and JOI claps his hands.

sample

3 1
1 2 1
2 1 1
2 10 1

0
1
1

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