Fixed-Length Paths II

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