Problem: 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.

Input

The first line contains two integers n and q (1 ≤ n, 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 ≤ u, v ≤ 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 ≤ v ≤ n, 0 ≤ d ≤ 10^7), representing a first-type operation. 
  * 2 v (1 ≤ v ≤ n), representing a second-type operation. 



It is guaranteed that there is at least one query of the second type.

Output

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 p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

Example

Input


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

Note

The image below shows the tree in the example:

<image>

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).

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(long long v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = v;
  }
  static int mod_inv(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  explicit operator long long() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val += other.val;
    if (val >= MOD) val -= MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return x % m;
    unsigned x_high = x >> 32, x_low = (unsigned)x;
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod((uint64_t)val * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  bool operator==(const _m_int &other) const { return val == other.val; }
  bool operator!=(const _m_int &other) const { return val != other.val; }
  _m_int inv() const { return mod_inv(val); }
  _m_int pow(long long p) const {
    assert(p >= 0);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      a *= a;
      p >>= 1;
    }
    return result;
  }
  friend ostream &operator<<(ostream &stream, const _m_int &m) {
    return stream << m.val;
  }
};
const int MOD = 998244353;
using mod_int = _m_int<MOD>;
template <typename T, bool maximum_mode = false>
struct RMQ {
  int n = 0, levels = 0;
  vector<T> values;
  vector<vector<int>> range_low;
  RMQ(const vector<T> &_values = {}) {
    if (!_values.empty()) build(_values);
  }
  static int largest_bit(int x) { return 31 - __builtin_clz(x); }
  int better_index(int a, int b) const {
    return (maximum_mode ? values[b] < values[a] : values[a] < values[b]) ? a
                                                                          : b;
  }
  void build(const vector<T> &_values) {
    values = _values;
    n = values.size();
    levels = largest_bit(n) + 1;
    range_low.resize(levels);
    for (int k = 0; k < levels; k++) range_low[k].resize(n - (1 << k) + 1);
    for (int i = 0; i < n; i++) range_low[0][i] = i;
    for (int k = 1; k < levels; k++)
      for (int i = 0; i <= n - (1 << k); i++)
        range_low[k][i] = better_index(range_low[k - 1][i],
                                       range_low[k - 1][i + (1 << (k - 1))]);
  }
  int query_index(int a, int b) const {
    assert(0 <= a && a < b && b <= n);
    int level = largest_bit(b - a);
    return better_index(range_low[level][a],
                        range_low[level][b - (1 << level)]);
  }
  T query_value(int a, int b) const { return values[query_index(a, b)]; }
};
struct LCA {
  int n = 0;
  vector<vector<int>> adj;
  vector<int> parent, depth, subtree_size;
  vector<int> euler, first_occurrence;
  vector<int> tour_start, tour_end, tour_list, postorder;
  vector<int> heavy_root;
  RMQ<int> rmq;
  LCA(int _n = 0) { init(_n); }
  LCA(const vector<vector<int>> &_adj) { init(_adj); }
  void init(int _n) {
    n = _n;
    adj.assign(n, {});
    parent.resize(n);
    depth.resize(n);
    subtree_size.resize(n);
    first_occurrence.resize(n);
    tour_start.resize(n);
    tour_end.resize(n);
    tour_list.resize(n);
    postorder.resize(n);
    heavy_root.resize(n);
  }
  void init(const vector<vector<int>> &_adj) {
    init(_adj.size());
    adj = _adj;
  }
  void add_edge(int a, int b) {
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  void dfs(int node, int par) {
    parent[node] = par;
    depth[node] = par < 0 ? 0 : depth[par] + 1;
    subtree_size[node] = 1;
    if (par >= 0)
      adj[node].erase(find(adj[node].begin(), adj[node].end(), par));
    for (int &child : adj[node]) {
      dfs(child, node);
      subtree_size[node] += subtree_size[child];
    }
    sort(adj[node].begin(), adj[node].end(),
         [&](int a, int b) { return subtree_size[a] > subtree_size[b]; });
  }
  int tour, post_tour;
  void tour_dfs(int node, bool heavy) {
    heavy_root[node] = heavy ? heavy_root[parent[node]] : node;
    first_occurrence[node] = euler.size();
    euler.push_back(node);
    tour_list[tour] = node;
    tour_start[node] = tour++;
    bool heavy_child = true;
    for (int child : adj[node]) {
      tour_dfs(child, heavy_child);
      euler.push_back(node);
      heavy_child = false;
    }
    tour_end[node] = tour;
    postorder[node] = post_tour++;
  }
  void build() {
    parent.assign(n, -1);
    for (int i = 0; i < n; i++)
      if (parent[i] < 0) dfs(i, -1);
    tour = post_tour = 0;
    for (int i = 0; i < n; i++)
      if (parent[i] < 0) {
        tour_dfs(i, false);
        euler.push_back(-1);
      }
    assert((int)euler.size() == 2 * n);
    vector<int> euler_depths;
    for (int node : euler)
      euler_depths.push_back(node < 0 ? node : depth[node]);
    rmq.build(euler_depths);
  }
  pair<int, int> find_farthest(int node, int par, int path) const {
    pair<int, int> current = {path, node};
    for (int neighbor : adj[node])
      if (neighbor != par)
        current = max(current, find_farthest(neighbor, node, path + 1));
    return current;
  }
  pair<int, pair<int, int>> get_diameter() const {
    int u = find_farthest(0, -1, 0).second;
    pair<int, int> farthest = find_farthest(u, -1, 0);
    int v = farthest.second;
    return {farthest.first, {u, v}};
  }
  int get_lca(int a, int b) const {
    a = first_occurrence[a];
    b = first_occurrence[b];
    if (a > b) swap(a, b);
    return euler[rmq.query_index(a, b + 1)];
  }
  bool is_ancestor(int a, int b) const {
    return tour_start[a] <= tour_start[b] && tour_start[b] < tour_end[a];
  }
  bool on_path(int x, int a, int b) const {
    return (is_ancestor(x, a) || is_ancestor(x, b)) &&
           is_ancestor(get_lca(a, b), x);
  }
  int get_dist(int a, int b) const {
    return depth[a] + depth[b] - 2 * depth[get_lca(a, b)];
  }
  int child_ancestor(int a, int b) const {
    assert(a != b);
    assert(is_ancestor(a, b));
    int child =
        euler[rmq.query_index(first_occurrence[a], first_occurrence[b] + 1) +
              1];
    assert(parent[child] == a);
    assert(is_ancestor(child, b));
    return child;
  }
  int get_kth_ancestor(int a, int k) const {
    while (a >= 0) {
      int root = heavy_root[a];
      if (depth[root] <= depth[a] - k) return tour_list[tour_start[a] - k];
      k -= depth[a] - depth[root] + 1;
      a = parent[root];
    }
    return a;
  }
  int get_kth_node_on_path(int a, int b, int k) const {
    int anc = get_lca(a, b);
    int first_half = depth[a] - depth[anc];
    int second_half = depth[b] - depth[anc];
    assert(0 <= k && k <= first_half + second_half);
    if (k < first_half)
      return get_kth_ancestor(a, k);
    else
      return get_kth_ancestor(b, first_half + second_half - k);
  }
  vector<pair<int, int>> compress_tree(vector<int> nodes) const {
    if (nodes.empty()) return {};
    auto &&compare_tour = [&](int a, int b) {
      return tour_start[a] < tour_start[b];
    };
    sort(nodes.begin(), nodes.end(), compare_tour);
    int k = nodes.size();
    for (int i = 0; i < k - 1; i++)
      nodes.push_back(get_lca(nodes[i], nodes[i + 1]));
    sort(nodes.begin(), nodes.end(), compare_tour);
    nodes.resize(unique(nodes.begin(), nodes.end()) - nodes.begin());
    vector<pair<int, int>> result = {{nodes[0], -1}};
    for (int i = 1; i < (int)nodes.size(); i++)
      result.emplace_back(nodes[i], get_lca(nodes[i], nodes[i - 1]));
    return result;
  }
};
struct query {
  int type, v;
  mod_int d;
};
int N, WORK_CUTOFF, Q;
LCA lca;
vector<mod_int> values, updates, query_d;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> N >> Q;
  WORK_CUTOFF = 1.25 * N;
  cerr << "Work cutoff: " << WORK_CUTOFF << endl;
  lca.init(N);
  for (int i = 0; i < N - 1; i++) {
    int u, v;
    cin >> u >> v;
    u--;
    v--;
    lca.add_edge(u, v);
  }
  lca.build();
  values.assign(N, 0);
  vector<query> pending_updates;
  mod_int inv_N = mod_int(1) / N;
  int work = 0;
  for (int q = 0; q < Q; q++) {
    query qry;
    cin >> qry.type >> qry.v;
    qry.v--;
    if (qry.type == 1) {
      int d;
      cin >> d;
      qry.d = d;
      pending_updates.push_back(qry);
    } else if (qry.type == 2) {
      mod_int answer = values[qry.v];
      for (query &prev : pending_updates)
        if (prev.v == qry.v) {
          answer += prev.d;
        } else if (lca.is_ancestor(prev.v, qry.v)) {
          int ca = lca.child_ancestor(prev.v, qry.v);
          mod_int probability = (N - lca.subtree_size[ca]) * inv_N;
          answer += probability * prev.d;
        } else {
          mod_int probability = lca.subtree_size[prev.v] * inv_N;
          answer += probability * prev.d;
        }
      work += pending_updates.size();
      cout << answer << '\n';
    } else {
      assert(false);
    }
    if (work >= WORK_CUTOFF) {
      updates.assign(N, 0);
      query_d.assign(N, 0);
      for (query &prev : pending_updates) query_d[prev.v] += prev.d;
      for (int node = 0; node < N; node++)
        if (query_d[node] != 0) {
          mod_int base_probability = lca.subtree_size[node] * inv_N;
          updates[0] += base_probability * query_d[node];
          updates[node] += (1 - base_probability) * query_d[node];
          for (int child : lca.adj[node])
            updates[child] -= lca.subtree_size[child] * inv_N * query_d[node];
        }
      for (int node : lca.tour_list) {
        values[node] += updates[node];
        for (int child : lca.adj[node]) updates[child] += updates[node];
      }
      pending_updates.clear();
      work = 0;
    }
  }
}