Blue vertex distance sums on a tree

There is a tree with $N$ vertices, numbered $0$ through $N-1$. Every edge has a length. The distance between two vertices is the sum of the edge lengths on the unique path that joins them.

At the start every vertex is white. Process the following two kinds of queries in the given order.

• Query 1: paint vertex $x$ blue. If vertex $x$ is already blue it stays blue, and it is still counted once.
• Query 2: compute the sum of the distances between vertex $x$ and every blue vertex. If vertex $x$ is itself blue, the distance $0$ is part of the sum. If no vertex is blue, the sum is $0$.

Write a program that answers every query 2.

The first line has the number of vertices $N$ ($2 \le N \le 100{,}000$) and the number of queries $Q$ ($1 \le Q \le 100{,}000$).

Each of the next $N-1$ lines has an edge as $u$, $v$, $w$: vertices $u$ and $v$ are joined by an edge of length $w$. ($0 \le u, v \le N-1$, $u \ne v$, $0 \le w \le 1{,}000{,}003$)

Each of the next $Q$ lines has one query. The first integer is the kind of the query, $1$ or $2$, and the second integer is $x$ ($0 \le x \le N-1$).

For each query 2, print its answer on its own line, in the order the queries are given.