B"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: 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 <= q n, q <= q 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 <= q u, v <= q 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: 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 <= x < M and x cdot q equiv p pmod{M} . The image below shows the tree in the example: For the first query, where v = 1 and d = 1 : 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 : Hence, the expected values of all vertices after this query are ( 2.2, 2.4, 2, 2, 2 ). "...