Lifeguard

Interview

Time limit1sMemory limit512 MB

Summary

The task is to count children farther than k meters from the lifeguard position.

Level: Easy1 of 10
Topics: Geometry, Math
Solved: No attempts yet

Problem

Children are spending their holidays at the seaside, and right now they are all bathing in the water. A lifeguard keeps them safe, and his range of sight is $k$ meters. Anyone located more than $k$ meters away from the lifeguard is invisible to him. Given the positions of the lifeguard and the children, determine how many children would not receive help if something dangerous happened.

Input

The first line contains integers $n$ , $k$ , $x$ , $y$ ( $1 \le n, k \le 100000$ , $0 \le x, y \le 10000$ ), denoting the number of children, the lifeguard's range of sight, and the lifeguard's position $(x, y)$ , respectively. Each of the next $n$ lines contains two integers $x_i$ and $y_i$ ( $0 \le x_i, y_i \le 10000$ ), the coordinates of the $i$ -th child. (The bathing area is described on a coordinate plane.)

Output

Print, on a single line, the number of children who cannot feel safe, that is, the number of children who lie outside the lifeguard's range of sight.

Examples2

Example 1
Input
```
5 3 2 2
2 4
2 6
3 3
4 2
5 6
```
Expected output
```
2
```
Example 2
Input
```
1 5 0 0
3 4
```
Expected output
```
0
```