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The K-th Distance

The K-th Distance

Time Limit: 8000/4000 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 27 Accepted Submission(s): 5

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

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