A15045 | Il Derby della Madonnina

The first line contains two integers $n$ and $v$ ( $1 \le n \le 2 \cdot 10^5$ , $1 \le v \le 10^6$ ) — the number of kicks that will take place and your maximum speed.

The second line contains $n$ integers $t_1, \ldots, t_n$ ( $1 \le t_i \le 10^9$ ) — the times of the kicks in the match. The sequence of times is guaranteed to be strictly increasing, i.e., $t_1 < t_2 < \cdots < t_n$ .

The third line contains $n$ integers $a_1, \ldots, a_n$ ( $-10^9 \le a_i \le 10^9$ ) — the positions along the touch-line where you have to be to monitor closely each kick.

Print the maximum number of kicks that you can monitor closely.

In the first sample, it is possible to move to the right at maximum speed for the first $3.5$ seconds and stay at position $7$ until the first kick happens, and then immediately move right also at maximum speed to watch the second kick at position $17$ . There is no way to monitor closely the third kick after the second kick, so at most $2$ kicks can be seen.