Number of pairs

Determine the number of vertex pairs that have a distance of exactly $l$.

Note that pairs $(u,v)$ and $(v,u)$ are considered identical.

Input Format

The first line contains two integers $n$ and $l$ $(1\le n\le 2\cdot 10^5,1\le l\le 10^6)$, representing the number of vertices and the specified distance, respectively.

Each of the following $n-1$ lines contains three integers $v_i$, $u_i$, and $t_i$ $(1\le u_i,v_i\le n,v_i\ne u_i,0\le t_i\le 10^6)$, which describe a road of length $t_i$ connecting cities $v_i$ and $u_i$.

Output Format

Print the number of vertex pairs that have a distance of exactly $l$.

Examples