Problem Statement

You are given two lists of integers, T and A, where:

1. t[i] represents the launch time of the i-th missile.
2. a[i] represents the position where you need to be to watch the i-th missile launch.

Starting at position 0, you can move up to X units per second. Your objective is to maximize the number of launches you can watch. You can watch a launch if you are at the required position a[i] exactly at the time t[i].

Input Format

The first line contains two integers N and X—the number of missile launches and your maximum speed.

The second line contains N integers t1, t2, ..., tn — the times of the launches in the mission in increasing order.

The third line contains N integers a1, a2, ..., an — the positions along the boundary where you need to be to watch each launch closely.

Output Format

Print the maximum number of launches that you can watch closely.

Constraints

• ( 1 \leq N \leq 2 \times 10^5 )
• ( 1 \leq X \leq 10^6 )
• ( 1 \leq t \leq 10^9 )
• ( -10^9 \leq a \leq 10^9 )

Sample Testcase 1

Input

1 2  
3  
7  

Output

0  

Explanation

He cannot reach any missile launch positions on time, so he can't watch any missile attacks.

Sample Testcase 2

Input

3 2  
5 10 15  
7 17 29  

Output

2  

Explanation

• Initial Position: Start at position 0.
• At time 5: Go to 7 with speed 2 for 3.5 seconds to reach there just in time to watch the missile launch.
• At time 10: Immediately move to 17 from 7, traveling at your maximum speed of 2 units per second, arriving precisely as the second launch occurs.
• Therefore, the maximum number of launches you can monitor closely is 2.