The buildings covered by the new safe area is called the safe buildings. Given the radius of the safe areas and the positions of the buildings, BaoBao wants to find all the buildings with the largest probability to become safe buildings.
There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:The first line contains three integers n (1 ≤ n ≤ 100),R and r(1 ≤ r ≤ R ≤ 104) , indicating the number of buildings and the radius of two safe circles.The following n lines each contains 2 integers xi and yi (−104 ≤ xi,yi ≤ 104) ,indicating the coordinate of the buildings. Here we assume that the center of the original safe circle is located at (0,0) , and all the buildings are inside the original circle.It's guaranteed that the sum of n over all test cases will not exceed 5000.
For each test case output two lines.
The first line contains an integer m, indicating the number of buildings with the highest probability to become safe buildings.
The second line contains m integers separated by a space in ascending order, indicating the indices of safest buildings.
Please, DO NOT output extra spaces at the end of each line.