The K-th Distance

Problem Description

Given a tree, which has n node in total. Define the distance between two node u and v is the number of edge on their unique route. So we can have n(n-1)/2 numbers for all the distance, then sort the numbers in ascending order. The task is to output the sum of the first K numbers.

 

Input

There are several cases, first is the number of cases T. (There are most twenty cases).
For each case, the first line contain two integer n and K (2≤n≤100000,0≤K≤min(n(n?1)/2,106) ). In following there are n-1 lines. Each line has two integer u , v. indicate that there is an edge between node u and v.

 

Output

For each case output the answer.

 

Sample Input

2
3 3
1 2
2 3
5 7
1 2
1 3
2 4
2 5

 

Sample Output

4
10

 

Source

BestCoder Round #17