Geometrical Voice

Time Limit: 3 Seconds    Memory Limit: 32768 KB

In Shiraz University, ACM director wants to inform the students about holding the ACM competition. To create a loud voice he uses an amplifier that distributes the sound on a circle with radius R.

In Shiraz University, students are strange. Whenever they hear some news about anything, they yell it instantly and the voice is distributed on a square with the center of their body. Before shouting, a special sense says them how much loud they should shout. The louder shouting, the larger size of the shouting-square will be achieved. The Length of the edges of the squares is always an integer number and the same for all the students. Each student is fixed in her place and the location of the amplifier is also given and fixed.

By having R, you should make a special sense for the students about the minimum size of their shouting-square such that at least k students can hear the news.

Input

There are multiple test cases. For each one, the first line contains three positive integers N (not greater than 10,000), R and k≤N, which indicate the number of students, the radius of the voice-circle of the amplifier and the minimum number of students, which should hear the news, respectively. Then in N following lines, each line contains two integers X_i and Y_i to represent the position of a student. The last line contains two integers X_A and Y_A representing the position of the amplifier. The absolute value of any integer in the input file will not exceed 1,000,000,000. The voice of the amplifier reaches to at least one student.

Output

For each test case, output the length of the edge of the sensed square in a separate line.

Sample Input

3 3 3
-1 1
1 -1
2 2
4 -1
6 2 6
0 2
-2 4
-4 3
-4 1
-4 -1
-2 -1
0 0

Sample Output

6
4

Submit

Source: 12th Iran Nationwide Internet Contest IV