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 \(1,2,…,n\).
• 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

Sample input

5 2 3
1 2
2 3
3 4
3 5

Sample output

6