A12996 · Tree Queries

题目描述

Hanh is a famous biologist. He loves growing trees and doing experiments on his own garden. One day, he got a tree consisting of $n$ vertices. Vertices are numbered from $1$ to $n$ . A tree with $n$ vertices is an undirected connected graph with $n-1$ edges. Initially, Hanh sets the value of every vertex to $0$ . Now, Hanh performs $q$ operations, each is either of the following types: - Type $1$ : Hanh selects a vertex $v$ and an integer $d$ . Then he chooses some vertex $r$ uniformly at random, lists all vertices $u$ such that the path from $r$ to $u$ passes through $v$ . Hanh then increases the value of all such vertices $u$ by $d$ . - Type $2$ : Hanh selects a vertex $v$ and calculates the expected value of $v$ . Since Hanh is good at biology but not math, he needs your help on these operations.

The first line contains two integers $n$ and $q$ ( $1 \leq n, q \leq 150\,000$ ) — the number of vertices on Hanh's tree and the number of operations he performs. Each of the next $n - 1$ lines contains two integers $u$ and $v$ ( $1 \leq u, v \leq n$ ), denoting that there is an edge connecting two vertices $u$ and $v$ . It is guaranteed that these $n - 1$ edges form a tree. Each of the last $q$ lines describes an operation in either formats: - $1$ $v$ $d$ ( $1 \leq v \leq n, 0 \leq d \leq 10^7$ ), representing a first-type operation. - $2$ $v$ ( $1 \leq v \leq n$ ), representing a second-type operation. It is guaranteed that there is at least one query of the second type.

For each operation of the second type, write the expected value on a single line. Let $M = 998244353$ , it can be shown that the expected value can be expressed as an irreducible fraction $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \not \equiv 0 \pmod{M}$ . Output the integer equal to $p \cdot q^{-1} \bmod M$ . In other words, output such an integer $x$ that $0 \le x < M$ and $x \cdot q \equiv p \pmod{M}$ .

输入 #1

输出 #1