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 $$987654319$$.