D. Tree Queriestime limit per test5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputHanh 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.InputThe 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.OutputFor 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}.ExampleInput
5 12
1 2
1 3
2 4
2 5
1 1 1
2 1
2 2
2 3
2 4
2 5
1 2 2
2 1
2 2
2 3
2 4
2 5
Output
1
199648871
399297742
199648871
199648871
598946614
199648873
2
2
2
NoteThe image below shows the tree in the example:  For the first query, where v = 1 and d = 1:   If r = 1, the values of all vertices get increased.  If r = 2, the values of vertices 1 and 3 get increased.  If r = 3, the values of vertices 1, 2, 4 and 5 get increased.  If r = 4, the values of vertices 1 and 3 get increased.  If r = 5, the values of vertices 1 and 3 get increased. Hence, the expected values of all vertices after this query are (1, 0.4, 0.8, 0.4, 0.4).For the second query, where v = 2 and d = 2:   If r = 1, the values of vertices 2, 4 and 5 get increased.  If r = 2, the values of all vertices get increased.  If r = 3, the values of vertices 2, 4 and 5 get increased.  If r = 4, the values of vertices 1, 2, 3 and 5 get increased.  If r = 5, the values of vertices 1, 2, 3 and 4 get increased. Hence, the expected values of all vertices after this query are (2.2, 2.4, 2, 2, 2).
5 12
1 2
1 3
2 4
2 5
1 1 1
2 1
2 2
2 3
2 4
2 5
1 2 2
2 1
2 2
2 3
2 4
2 5

1 199648871 399297742 199648871 199648871 598946614 199648873 2 2 2 
['data structures', 'probabilities', 'trees', '*2700']