Given a weighted tree ($T$) and an integer $MAXW$, count the number of weighted graphs whose non-negative edges weight at most $MAXW$ and $T$ is an MST (minimum spanning tree) for that graph. Output the result modulo $987654319$.

Input

The first line of input contains two integers $n$ and $MAXW$, the number of vertices of the aforementioned tree and the maximum allowed weight of an edge respectively ($1 \le n \le 300000$).

The next $n-1$ lines describes the tree. Each of which contain three integers, $v_i$, $u_i$ and $w_i$, meaning that there's and edge connecting vertices $v_i$ and $u_i$ with weight equal to $w_i$ ($0 \le MAXW, w_i \le 10^9$).

It's guaranteed that the given graph forms a tree.

Output

Print only one integer, the number of desired graphs modulo $987654319$.