Background

The comfort we can seek, after much thought, is still the hope for the future.

Hope is attached to existence; where there is existence, there is hope; where there is hope, there is light.

Problem Description

Sulawesi. The Earth is $L$ units of time away from entering Jupiter's Roche limit.

Caide Ren received the "Ignite Jupiter Plan" from Ailifen. The plan requires him to gather all rescue teams at the same steering engine, clear obstacles, and use the "Spring Festival Twelve-Blast" program to control the engine to ignite Jupiter.

There are $n$ steering engines, connected by $n - 1$ roads. Any two steering engines can reach each other through roads, and the distance between them is the number of edges on their shortest path.

A total of $k$ rescue teams $s_1, s_2, ..., s_k$ are deployed nearby, each with a rescue range. The rescue range is a connected subset of the steering engine set, where all engines on the roads between any two engines in the range are also within the rescue range.

We say that an engine $u$ can be reached by a rescue team with range $S$ if and only if $u$ is in $S$, and the distance from any engine $v$ in $S$ to $u$ is not greater than $L$. This ensures that no matter where the rescue team is within their range, they can reach engine $u$ before time runs out.

Caide Ren needs to command the $k$ rescue teams to concentrate at the same engine. However, due to communication breakdown, he does not know the rescue range of each team. He wants to calculate the number of feasible dispatch plans and inputs the problem into the computer.

On the other side of this computer—you, need to help him count how many possible deployment plans exist where there is an engine that can be reached by all rescue teams. A plan refers to a set of rescue ranges $\{S_1, S_2, ..., S_k\}$; two plans are different if and only if the rescue range $S_i$ of some rescue team $s_i$ is different between them. In this joint government-planned saturation rescue, the rescue ranges of two teams may intersect or even be identical.

You know the answer is very large. The snowmobiles穿梭 through tens of thousands of landmarks, the possible rescue ranges are vast, but the plans to gather all teams are few. You don't have time to despair, let alone calculate that number.

You can only calculate the result modulo $998244353$.

That is hope.

Even if it requires modulo, it is light.

Input Format

The first line contains three numbers $n$, $L$, and $k$, representing the number of steering engines, the remaining time to save Earth, and the number of rescue teams, respectively.

The next $n - 1$ lines each contain two integers $u$ and $v$, indicating that there is a road connecting the $u$-th and $v$-th steering engines.

Output Format

A single integer representing the number of plans modulo $998244353$.

Sample Input and Output

Input Sample #1

2 1 2
1 2

Output Sample #1

7

Input Sample #2

4 1 1
1 2
2 3
3 4

Output Sample #2

9

Input Sample #3

5 1 1
1 2
1 3
2 4
2 5

Output Sample #3

14

Input Sample #4

12 2 10
1 2
2 3
3 5
4 5
5 7
6 7
7 8
8 9
9 10
9 11
11 12

Output Sample #4

953325149

Notes

Sample 1 Explanation

There are the following feasible plans:

Sample 2 Explanation

With only one rescue team, all plans except where the rescue range is the entire set $\{1,2,3,4\}$ are feasible.

Sample 4 Explanation

The graph for this test case is shown below:

Subtasks

For all data, $1 \leqslant n \leqslant 10^6$, $0 \leqslant L \leqslant n$, $1 \leqslant k \leqslant 10$.

Caide Ren looks up. It's a sight he's never seen before—Jupiter occupies most of the sky, its vibrant colors piercing through the thin atmosphere,格外刺眼。

A small boat adrift in the boundless ocean,不知何时就会被狂风所倾覆；而船上平凡的我们，也只能怀着渺茫的希望，跟随着舵手指引的航向前行吧。

He steps forward and presses $\texttt{Enter}$.

$ sudo ./spring12biubiu

The command has been issued.

见题面 Input 部分

见题面 Output 部分