You are given a tree with nn vertices (numbered 1,2,…,n1,2,…,n) and an integer kk.

A subtree is defined as a connected subgraph of the tree. That is, a subtree is another tree that can be obtained by removing some (possibly none) vertices and all edges incident to those vertices from TT.

A subset SS of vertices is called good if every subtree containing all the nodes in SS has at least kk nodes.

Find the **size of the smallest good subset**.

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### Input

- The first line contains a single integer TT, the number of test cases. The descriptions of test cases follow.
- The first line of each testcase contains two integers, nn and kk.
- The next n−1n−1 lines each contains two integers uu, vv, denoting an edge between vertices uu and vv of the tree.

### Output

- For each test case print in a single line, the minimum size of a good subset.

### Constraints

- 1≤n≤1051≤n≤105
- 1≤k≤n1≤k≤n
- 1≤u,v≤n1≤u,v≤n
- The given edges for each test case form a tree.
- The sum of nn over all test cases is at most 106106.

### Subtasks

**Subtask #1 (30 points):** 1≤n≤1031≤n≤103

**Subtask #2 (70 points):** original constraints

### Sample Input

```
2
7 5
1 2
2 3
3 4
3 5
5 6
3 7
6 4
1 2
1 3
1 4
1 5
1 6
```

### Sample Output

```
2
3
```

### Explanation

**Test Case 11:** Consider the set S={1,6}S={1,6}.

The smallest subtree that contains both of the vertices in SS is the path between them (1→2→3→5→61→2→3→5→6) which contains 55 vertices. Hence for k=5k=5, the answer is 22.

**Test Case 22:** Consider the set S={2,3,4}S={2,3,4}.

The smallest subtree that contains these three vertices includes 44 nodes {1,2,3,4}{1,2,3,4}.

**Solution**

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rookieThe previos solution of min dual area code is running only sample cases not test cases

AdminWe will update the code if there is an issue.

ShreyMimimum subtree cover is giving wrong answer can you tell me error.

AdminSend your code @ thunderbitzbusiness@gmail.com