Given a tree of $n$ vertices. Count the number of simple paths with length $k$.
### Input
- The first line contains an integer $n$.
- The next $n - 1$ lines, each line contains 2 integers $u, v$, there is an edge between $u$ and $v$.
### Output
- Print the number of paths with length $k$.
### Constraints
- $1 \le k \le n \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
5 2
1 2
2 3
1 4
4 5
```
Output:
```
3
```
