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.

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 $b$ .

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

Print one integer: the number of paths.