D. Mines
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There are $$$n$$$ mines installed along the straight road. Mine number $$$i$$$ is located at the coordinate $$$x_i$$$ and has a blast radius of $$$d_i$$$. When this mine explodes, all mines with coordinates from $$$x_i - d_i$$$ to $$$x_i + d_i$$$ inclusive will also explode (and they, in turn, may cause other mines to explode, and so on).

Determine how many mines will explode in total if mine number $$$k$$$ is detonated.

Input

The first line of input contains an integer $$$n$$$ ($$$1 \le n \le 10^5$$$).

The second line contains $$$n$$$ distinct integers $$$x_1$$$, $$$x_2$$$, ..., $$$x_n$$$ in increasing order ($$$0 \le x_i \le 10^9$$$).

The third line contains $$$n$$$ integers $$$d_1$$$, $$$d_2$$$, ..., $$$d_n$$$ ($$$0 \le d_i \le 10^9$$$).

The fourth line contains an integer $$$k$$$ ($$$1 \le k \le n$$$).

Output

Output a single integer — the number of exploded mines.

Example
Input
5
0 10 30 50 100
40 10 25 20 10
2
Output
4
Note

In the example, the second mine will cause the first to explode, the first will cause the third to explode, and the third will cause the fourth to explode.