F. K-Star Sets
time limit per test
3 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

Let $$$k \geq 2$$$. Define a $$$k$$$-star as a tree with $$$k+1$$$ nodes, such that there is one central node connected to exactly $$$k$$$ leaves. A $$$k$$$-star set is a non-empty graph where each connected component of that graph is a $$$k$$$-star. For a given tree, count the number of subsets of edges, such that the graph composed of just those edges and nodes that are endpoints of those edges forms a $$$k$$$-star set.

Input

The first line of input consists of two integers $$$n$$$ and $$$k$$$ ($$$2 \leq k \lt n \leq 2 \cdot 10^5$$$) — the number of nodes in the given tree and the size of each target star.

The following $$$n-1$$$ lines each consist of two integers $$$u$$$ and $$$v$$$ ($$$1 \leq u, v \leq n$$$), denoting that there is an edge between nodes $$$u$$$ and $$$v$$$.

Output

Output a single integer denoting the number of $$$k$$$-star sets of the given tree. Since this number can be large, output the answer under modulo $$$998244353$$$.

Examples
Input
5 3
1 5
2 5
3 5
4 5
Output
4
Input
7 2
1 2
1 3
2 4
3 5
3 6
3 7
Output
11