## Description:

Consider a un-rooted tree T which is not the biological significance of tree or plant, but a tree as an undirected graph in graph theory with n nodes, labelled from 1 to n. If you cannot understand the concept of a tree here, please omit this problem.

Now we decide to colour its nodes with k distinct colours, labelled from 1 to k. Then for each colour i = 1, 2, ・ ・ ・ , k, define Ei as the minimum subset of edges connecting all nodes coloured by i. If there is no node of the tree coloured by a specified colour i, Ei will be empty.

Try to decide a colour scheme to maximize the size of E1 ∩ E2 ・ ・ ・ ∩ Ek, and output its size.

## Input:

The first line of input contains an integer T (1 ≤ T ≤ 1000), indicating the total number of test cases.

For each case, the first line contains two positive integers n which is the size of the tree and k (k ≤ 500) which is the number of colours. Each of the following n - 1 lines contains two integers x and y describing an edge between them. We are sure that the given graph is a tree.

The summation of n in input is smaller than or equal to 200000.

## Output:

For each test case, output the maximum size of E1 ∩ E1 ... ∩ Ek.

## Sample Input:

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

## Sample Output:

1
0
1