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;
const int MOD = 998244353;
template <typename T>
struct modular {
  constexpr modular() : val(0) {}
  constexpr modular(const modular<T>& _m) : val(_m.val) {}
  template <typename U>
  constexpr modular(const U& _r = U()) {
    val = -MOD <= _r && _r < MOD ? _r : _r % MOD;
    if (val < 0) {
      val += MOD;
    }
  }
  const T operator()() { return val; }
  template <typename U>
  explicit operator U() const {
    return static_cast<U>(val);
  }
  modular<T>& operator+=(const modular<T>& _m) {
    if ((val += _m.val) >= MOD) {
      val -= MOD;
    }
    return *this;
  }
  modular<T>& operator-=(const modular<T>& _m) {
    if ((val -= _m.val) < 0) {
      val += MOD;
    }
    return *this;
  }
  modular<T>& operator*=(const modular<T>& _m) {
    val = modular<T>(static_cast<int64_t>(val) * static_cast<int64_t>(_m.val))
              .val;
    return *this;
  }
  modular<T>& operator/=(const modular<T>& _m) {
    T a = _m.val, b = MOD, u = 0, v = 1;
    while (a != 0) {
      T q = b / a;
      b -= q * a;
      swap(a, b);
      u -= q * v;
      swap(u, v);
    }
    return *this *= u;
  }
  modular<T>& operator=(const modular<T>& _m) {
    val = _m.val;
    return *this;
  }
  template <typename U>
  modular<T>& operator+=(const U& _r) {
    return *this += modular<T>(_r);
  }
  template <typename U>
  modular<T>& operator-=(const U& _r) {
    return *this -= modular<T>(_r);
  }
  template <typename U>
  modular<T>& operator*=(const U& _r) {
    return *this *= modular<T>(_r);
  }
  template <typename U>
  modular<T>& operator/=(const U& _r) {
    return *this /= modular<T>(_r);
  }
  template <typename U>
  modular<T>& operator=(const U& _r) {
    val = modular<T>(_r).val;
    return *this;
  }
  modular<T> operator-() { return modular<T>(-val); }
  template <typename U>
  friend bool operator==(const modular<U>&, const modular<U>&);
  friend std::istream& operator>>(std::istream& os, modular<T>& _m) {
    os >> _m.val;
    _m *= 1;
    return os;
  }
  friend std::ostream& operator<<(std::ostream& os, const modular<T>& _m) {
    return os << _m.val;
  }
  template <typename U>
  modular<T> exp(U e) {
    modular<T> res = 1;
    modular<T> b = val;
    if (e < 0) {
      b = 1 / b;
      e *= -1;
    }
    for (; e; e >>= 1) {
      if (e & 1) {
        res *= b;
      }
      b *= b;
    }
    return res;
  }

 private:
  T val;
};
template <typename T>
inline modular<T> operator+(const modular<T>& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) += _rhs;
}
template <typename T, typename U>
inline modular<T> operator+(const modular<T>& _lhs, const U& _rhs) {
  return modular<T>(_lhs) += _rhs;
}
template <typename T, typename U>
inline modular<T> operator+(const U& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) += _rhs;
}
template <typename T>
inline modular<T> operator-(const modular<T>& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) -= _rhs;
}
template <typename T, typename U>
inline modular<T> operator-(const modular<T>& _lhs, const U& _rhs) {
  return modular<T>(_lhs) -= _rhs;
}
template <typename T, typename U>
inline modular<T> operator-(const U& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) -= _rhs;
}
template <typename T>
inline modular<T> operator*(const modular<T>& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) *= _rhs;
}
template <typename T, typename U>
inline modular<T> operator*(const modular<T>& _lhs, const U& _rhs) {
  return modular<T>(_lhs) *= _rhs;
}
template <typename T, typename U>
inline modular<T> operator*(const U& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) *= _rhs;
}
template <typename T>
inline modular<T> operator/(const modular<T>& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) /= _rhs;
}
template <typename T, typename U>
inline modular<T> operator/(const modular<T>& _lhs, const U& _rhs) {
  return modular<T>(_lhs) /= _rhs;
}
template <typename T, typename U>
inline modular<T> operator/(const U& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) /= _rhs;
}
template <typename T>
inline bool operator==(const modular<T>& _lhs, const modular<T>& _rhs) {
  return _lhs.val == _rhs.val;
}
template <typename T, typename U>
inline bool operator==(const modular<T>& _lhs, const U& _rhs) {
  return _lhs == modular<T>(_rhs);
}
template <typename T, typename U>
inline bool operator==(const U& _lhs, const modular<T>& _rhs) {
  return modular<T>(_lhs) == _rhs;
}
template <typename T>
inline bool operator!=(const modular<T>& _lhs, const modular<T>& _rhs) {
  return !(_lhs == _rhs);
}
template <typename T, typename U>
inline bool operator!=(const modular<T>& _lhs, const U& _rhs) {
  return !(_lhs == _rhs);
}
template <typename T, typename U>
inline bool operator!=(const U& _lhs, const modular<T>& _rhs) {
  return !(_lhs == _rhs);
}
template <typename T = int>
struct Fenwick {
  int n;
  vector<T> v;
  Fenwick(int size = 100005) : n(size), v(n + 1, 0) {}
  inline void add(int p, T val) {
    for (; p <= n; p += (p & -p)) {
      v[p] += val;
    }
  }
  inline T query(int p) {
    T tmp = 0;
    for (; p > 0; p -= (p & -p)) {
      tmp += v[p];
    }
    return tmp;
  }
  inline T query(int l, int r) { return query(r) - query(l - 1); }
};
template <typename T>
struct RASQ {
  int n;
  Fenwick<T> diff;
  RASQ(int _n) : n(_n), diff(n) {}
  inline void add(int l, int r, T val) {
    diff.add(l, val);
    diff.add(r, -val);
  }
  inline T query(int p) { return diff.query(p); }
};
struct HLD {
  int n;
  vector<vector<int>> g;
  vector<int> sz, pa, depth, sta, fin, heavy, top, tour;
  int tim;
  RASQ<modular<int>> ra;
  vector<modular<int>> buf;
  HLD(int _n)
      : n(_n),
        g(n),
        sz(n, 1),
        pa(n, -1),
        depth(n),
        sta(n),
        fin(n),
        heavy(n, -1),
        top(n),
        ra(n),
        buf(n) {
    tour.reserve(n);
  }
  inline void add(int u, int v) {
    g[u].emplace_back(v);
    g[v].emplace_back(u);
  }
  void dfs(int u) {
    if (pa[u] != -1) g[u].erase(find(g[u].begin(), g[u].end(), pa[u]));
    for (int& v : g[u]) {
      pa[v] = u;
      depth[v] = depth[u] + 1;
      dfs(v);
      sz[u] += sz[v];
      if (sz[v] > sz[g[u][0]]) swap(v, g[u][0]);
    }
  }
  void hld(int u) {
    sta[u] = tim++;
    tour.emplace_back(u);
    for (int v : g[u]) {
      top[v] = (v == g[u][0] ? heavy[u] = v, top[u] : v);
      hld(v);
    }
    fin[u] = tim;
  }
  void build(int root = 0) {
    dfs(root);
    tim = 1;
    top[root] = root;
    hld(root);
  }
  inline void across_light(int& v) { v = pa[top[v]]; }
  int lca(int u, int v) {
    while (top[u] != top[v]) {
      sta[u] < sta[v] ? across_light(v) : across_light(u);
    }
    return sta[u] < sta[v] ? u : v;
  }
  using F = function<void(int, int)>;
  void for_v_path(int u, int v, F f) {
    while (true) {
      if (sta[u] > sta[v]) swap(u, v);
      f(max(sta[top[v]], sta[u]), sta[v] + 1);
      if (top[u] == top[v]) return;
      across_light(v);
    }
  }
  void for_v_sub(int u, F f, bool exclude = 0) { f(sta[u] + exclude, fin[u]); }
  void update(int u, modular<int> d) {
    buf[u] += d;
    if (heavy[u] != -1) {
      int v = heavy[u];
      modular<int> prob = (n - sz[v]) * d;
      for_v_sub(v, [&](int l, int r) { ra.add(l, r, prob); });
    }
    modular<int> prob = sz[u] * d;
    for_v_sub(0, [&](int l, int r) { ra.add(l, r, prob); });
    for_v_sub(u, [&](int l, int r) { ra.add(l, r, -prob); });
    ra.add(sta[u], sta[u] + 1, n * d);
  }
  modular<int> query(int u) {
    modular<int> res = ra.query(sta[u]);
    int x = u, p;
    while (x != -1) {
      x = top[x];
      p = pa[x];
      if (p != -1) res += buf[p] * (n - sz[x]);
      x = p;
    }
    return res;
  }
  void process_query(int q) {
    modular<int> Q = modular<int>(1) / n;
    while (q--) {
      int op;
      cin >> op;
      if (op == 1) {
        int u, d;
        cin >> u >> d;
        u--;
        update(u, d);
      } else {
        int u;
        cin >> u;
        u--;
        cout << query(u) * Q << "\n";
      }
    }
  }
};
void solve() {
  int n, q;
  cin >> n >> q;
  HLD hld(n);
  for (int _ = 1; _ < n; _++) {
    int x, y;
    cin >> x >> y;
    x--;
    y--;
    hld.add(x, y);
  }
  hld.build();
  hld.process_query(q);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  solve();
  cout << endl;
}