**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