**Time limit:**1.00 s**Memory limit:**512 MB

**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`