CSES - Fixed-Length Paths II
  • Time limit: 1.00 s
  • Memory limit: 512 MB
Given a tree of $n$ nodes, your task is to count the number of distinct paths that have at least $k_1$ and at most $k_2$ edges.

Input

The first input line contains three integers $n$, $k_1$ and $k_2$: the number of nodes and the path lengths. The nodes are numbered $1,2,\ldots,n$.

Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Output

Print one integer: the number of paths.

Constraints
  • $1 \le k_1 \le k_2 \le n \le 2 \cdot 10^5$
  • $1 \le a,b \le n$
Example

Input:
5 2 3
1 2
2 3
3 4
3 5


Output:
6