P12537 [XJTUPC 2025] Gros-Phi

Awa is participating in a live music game called Gros-Phi. In the event, Awa must appear at a specified location at a specified time. Specifically, Gros-Phi's activity area is an infinitely long straight line. Gros-Phi has a total of $n$ scoring points. The $i$-th scoring point requires Awa to appear at position $x_i$ at time $t_i$. Awa's maximum running speed is $v$ units per moment. At time $0$, Awa can choose any position and then start playing Gros-Phi. Awa wants to know how many scoring points she can reach at most.

The first line contains a positive integer $T$ ($1\le T \le 5\times 10^5$), indicating that Awa played a total of $T$ games. For each game, the first line contains two positive integers $n$ and $v$ ($1\le n \le 5\times 10^5$, $1 \le v \le 10^9$), separated by a space, indicating the number of decision points and the maximum speed of Awa. The next $n$ lines, each containing two integers $t_i$ and $x_i$ ($0 \le t_i, |x_i| \le 10^9$), separated by a space, describe a scoring point. It is guaranteed that there are no two identical scoring points in a game. It is guaranteed that the sum of $n$ in $T$ rounds of games does not exceed $5 \times 10^5$.

There should be $T$ lines in total, each line contains one integer, indicating how many scoring points Awa can reach at most in the corresponding game.

Since the input and output data of this question are large, it is recommended to use a faster input and output method, such as $\tt{scanf}$ and $\tt{printf}$.