One Goal

There are $n$ cities and $n - 1$ roads in the Republic of Never. The cities are numbered from 1 to $n$. Every road connects two cities and can be traversed in both directions. Any two cities can reach each other using the roads. The distance $d(u, v)$ is the smallest number of roads needed to travel from city $u$ to city $v$.

There are $k$ friends who want to meet. The $i$-th friend lives in city $a_i$. The friends choose city $v$ such that $\sum_{i=1}^{k}{d(v, a_i)}$ is minimum. If several cities achieve this minimum, they choose the one with the smallest number.

You do not know where the friends live. Each friend may live in any of the $n$ cities, so there are $n^k$ possible cases. Find the sum of the numbers of the cities the friends choose over all $n^k$ cases. Print the sum modulo 998244353.

The first line contains two integers $n$ and $k$ ($2 \le n, k \le 30000$). Each of the following $n - 1$ lines contains two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$, $u_i \ne v_i$), the numbers of the cities connected by the $i$-th road. It is guaranteed that any two cities can reach each other using the roads.

Print the sum of the numbers of the chosen cities over all $n^k$ cases, modulo 998244353.

In the first example, there are 3 cities and 2 friends, so there are $3^2 = 9$ cases. In three of them, both friends live in the same city, and they choose that city. In the other six, the friends live in different cities, and they choose city 1. The total is $(1 + 2 + 3) + 6 \cdot 1 = 12$.