Revenge of kNN

In pattern recognition, the k-Nearest Neighbors algorithm (or k-NN for short) is a non-parametric method used for classification and regression. In both cases, the input consists of the k closest training examples in the feature space.
In k-NN regression, the output is the property value for the object. This value is the average of the values of its k nearest neighbors.
---Wikipedia

Today, kNN takes revenge on you. You have to handle a kNN case in one-dimensional coordinate system. There are N points with a position Xi and value Vi. Then there are M kNN queries for point with index i, recalculate its value by averaging the values its k-Nearest Neighbors. Note you have to replace the value of i-th point with the new calculated value. And if there is a tie while choosing k-Nearest Neighbor, choose the one with the minimal index first.

The first line contains a single integer T, indicating the number of test cases.

Each test case begins with three integers N, M and K, in which K indicating the number of k-Nearest Neighbors. Then N lines follows, each line contains two integers Xi and Vi. Then M lines with the queried index Qi follows.

[Technical Specification]
1. 1 <= T <= 5
2. 2<=N<= 100 000, 1<=M<=100 000
3. 1 <= K <= min(N – 1, 10)
4. 1 <= Vi <= 1 000
5. 1 <= Xi <= 1 000 000 000, and no two Xi are identical.
6. 1 <= Qi <= N

For each test case, output sum of all queries rounded to six fractional digits.

1
5 3 2
1 2
2 3
3 6
4 8
5 8
2
3
4

17.000000

For the first query, the 2-NN for point 2 is point 1 and 3, so the new value is (2 + 6) / 2 = 4.
For the second query, the 2-NN for point 3 is point 2 and 4, and the value of point 2 is changed to 4 by the last query, so the new value is (4 + 8) / 2 = 6.

Huge input, faster I/O method is recommended.

BestCoder Round #9