#include <bits/stdc++.h>
using namespace std;
const int max_n = 1e5 + 10, inf = 1000111222;
const int max_lev = 18;
class tree {
 public:
  int tin[max_n], tout[max_n];
  int h[max_n];
  int p[max_lev][max_n];
  void init(int n, vector<int> g[], int root = 0) {
    curt = -1;
    for (int i = 0; i < max_lev; ++i) {
      p[i][root] = root;
    }
    dfs(root, g);
    get_all_p(n);
  }
  bool is_ancestor(int u, int v) const {
    return tin[u] <= tin[v] && tout[u] >= tout[v];
  }
  bool is_on_path(int u, int v, int lca, int q) {
    return is_ancestor(lca, q) && (is_ancestor(q, u) || is_ancestor(q, v));
  }
  bool is_edge_on_path(int u, int v, int lca, int q1, int q2) {
    return is_on_path(u, v, lca, q1) && is_on_path(u, v, lca, q2);
  }
  int lca(int u, int v) const {
    if (is_ancestor(u, v)) {
      return u;
    }
    for (int i = max_lev - 1; i >= 0; --i) {
      if (!is_ancestor(p[i][u], v)) {
        u = p[i][u];
      }
    }
    return p[0][u];
  }
  int get_dist(int u, int v) const {
    const int lc = lca(u, v);
    return h[u] + h[v] - 2 * h[lc];
  }
  int get_up(int v, int dist) const {
    for (int i = max_lev - 1; i >= 0; --i) {
      if (get_bit(dist, i)) {
        v = p[i][v];
      }
    }
    return v;
  }

 protected:
  void dfs(int v, vector<int> g[]) {
    tin[v] = ++curt;
    for (int to : g[v]) {
      if (to == p[0][v]) {
        continue;
      }
      p[0][to] = v;
      h[to] = h[v] + 1;
      dfs(to, g);
    }
    tout[v] = curt;
  }
  void get_all_p(int n) {
    for (int lev = 1; lev < max_lev; ++lev) {
      for (int i = 0; i < n; ++i) {
        p[lev][i] = p[lev - 1][p[lev - 1][i]];
      }
    }
  }
  static bool get_bit(int mask, int pos) { return (mask >> pos) & 1; }
  int curt;
};
class heavy_light_tree : public tree {
 public:
  int up[max_n], sz[max_n];
  vector<int> order;
  void init(int n, vector<int> g[], int root = 0) {
    curt = -1;
    for (int i = 0; i < max_lev; ++i) {
      p[i][root] = root;
    }
    reorder_subtrees(root, -1, g);
    up[root] = root;
    dfs(root, g);
    get_all_p(n);
  }
  template <bool lca_inclusive, typename Callback>
  void decompose_on_paths(int v1, int v2, Callback &callback) const {
    const int lc = lca(v1, v2);
    vertical_decompose_on_paths<lca_inclusive>(v1, lc, callback);
    vertical_decompose_on_paths<false>(v2, lc, callback);
  }
  template <bool lca_inclusive>
  vector<pair<int, int>> decompose_on_paths(int v1, int v2) const {
    vector<pair<int, int>> res;
    auto callback = [&res](int l, int r) { res.emplace_back(l, r); };
    decompose_on_paths<lca_inclusive>(v1, v2, callback);
    return res;
  }
  vector<int> get_light_edges_down(int u, int v, int lca) const {
    vector<int> res;
    lol_kek(u, lca, res);
    lol_kek(v, lca, res);
    return res;
  }
  void lol_kek(int v, int parent, vector<int> &res) const {
    while (true) {
      if (is_ancestor(up[v], parent)) {
        return;
      }
      res.push_back(up[v]);
      v = p[0][up[v]];
    }
  }

 private:
  template <bool parent_inclusive, typename Callback>
  void vertical_decompose_on_paths(int v, int parent,
                                   Callback &callback) const {
    while (true) {
      if (is_ancestor(up[v], parent)) {
        const int l = tin[parent] + !parent_inclusive, r = tin[v];
        if (l <= r) {
          callback(l, r);
        }
        return;
      }
      callback(tin[up[v]], tin[v]);
      v = p[0][up[v]];
    }
  }
  void reorder_subtrees(int v, int p, vector<int> g[]) {
    sz[v] = 1;
    for (int i = 0; i < g[v].size(); ++i) {
      if (g[v][i] == p) {
        swap(g[v][i], g[v].back());
        g[v].pop_back();
        break;
      }
    }
    for (int to : g[v]) {
      reorder_subtrees(to, v, g);
      sz[v] += sz[to];
    }
    for (int i = 1; i < g[v].size(); ++i) {
      if (sz[g[v][i]] > sz[g[v][0]]) {
        swap(g[v][i], g[v][0]);
      }
    }
  }
  void dfs(int v, vector<int> g[]) {
    order.push_back(v);
    tin[v] = ++curt;
    sz[v] = 1;
    for (int to : g[v]) {
      if (to == p[0][v]) {
        continue;
      }
      up[to] = to;
      if (to == g[v][0]) {
        up[to] = up[v];
      }
      p[0][to] = v;
      h[to] = h[v] + 1;
      dfs(to, g);
      sz[v] += sz[to];
    }
    tout[v] = curt;
  }
};
vector<int> reb[max_n];
int a[max_n];
heavy_light_tree T;
const int magic = 300;
int type[max_n];
int A[max_n];
int B[max_n];
long long pref_value[max_n];
void dfs_push_value(int now) {
  for (auto wh : reb[now]) {
    pref_value[wh] += pref_value[now];
    dfs_push_value(wh);
  }
}
bool mark[max_n];
pair<bool, int> G[max_n];
int G_T;
bool get_G(int a) {
  if (G[a].second < G_T) {
    G[a].first = 0;
    G[a].second = G_T;
  }
  return G[a].first;
}
void set_G(int a, bool val) {
  if (G[a].second < G_T) {
    G[a].first = 0;
    G[a].second = G_T;
  }
  G[a].first = val;
}
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  for (int i = 1; i < n; i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    u--;
    v--;
    reb[u].push_back(v);
    reb[v].push_back(u);
  }
  T.init(n, reb, 0);
  for (int i = 0; i < q; i++) {
    scanf("%d%d%d", &type[i], &A[i], &B[i]);
    if (type[i] == 1) {
      A[i]--;
    } else {
      A[i]--;
      B[i]--;
    }
  }
  auto get_edge_w = [&](int a, int b) { return max(abs(a + b), abs(a - b)); };
  for (int i = 0; i < q; i += magic) {
    int L = i;
    int R = min(q, i + magic);
    memset(mark, 0, sizeof(mark));
    vector<int> cur_mark;
    for (int j = L; j < R; j++) {
      if (type[j] == 1) {
        mark[A[j]] = 1;
        cur_mark.push_back(A[j]);
      }
    }
    sort(cur_mark.begin(), cur_mark.end());
    cur_mark.resize(unique(cur_mark.begin(), cur_mark.end()) -
                    cur_mark.begin());
    memset(pref_value, 0, sizeof(pref_value));
    for (int i = 1; i < n; i++) {
      if (!mark[i] && !mark[T.p[0][i]]) {
        pref_value[i] = get_edge_w(a[i], a[T.p[0][i]]);
      }
    }
    dfs_push_value(0);
    for (int j = L; j < R; j++) {
      if (type[j] == 1) {
        a[A[j]] = B[j];
      } else {
        int u = A[j];
        int v = B[j];
        int lca = T.lca(u, v);
        long long ans = 0;
        ans += pref_value[u];
        ans += pref_value[v];
        ans -= 2 * pref_value[lca];
        G_T++;
        for (auto marked : cur_mark) {
          if (marked != 0 && (mark[marked] || mark[T.p[0][marked]]) &&
              get_G(marked) == 0 &&
              T.is_edge_on_path(u, v, lca, marked, T.p[0][marked])) {
            set_G(marked, 1);
            ans += get_edge_w(a[marked], a[T.p[0][marked]]);
          }
          if ((int)(reb[marked].size()) != 0) {
            marked = reb[marked][0];
            if (marked != 0 && (mark[marked] || mark[T.p[0][marked]]) &&
                get_G(marked) == 0 &&
                T.is_edge_on_path(u, v, lca, marked, T.p[0][marked])) {
              set_G(marked, 1);
              ans += get_edge_w(a[marked], a[T.p[0][marked]]);
            }
          }
        }
        auto lol = T.get_light_edges_down(u, v, lca);
        for (auto marked : lol) {
          if (marked != 0 && (mark[marked] || mark[T.p[0][marked]]) &&
              get_G(marked) == 0 &&
              T.is_edge_on_path(u, v, lca, marked, T.p[0][marked])) {
            set_G(marked, 1);
            ans += get_edge_w(a[marked], a[T.p[0][marked]]);
          }
        }
        cout << ans << "\n";
      }
    }
  }
}

### Prompt

Create a solution in Cpp for the following problem:

Chanek Jones is back, helping his long-lost relative Indiana Jones, to find a secret treasure in a maze buried below a desert full of illusions.

The map of the labyrinth forms a tree with n rooms numbered from 1 to n and n - 1 tunnels connecting them such that it is possible to travel between each pair of rooms through several tunnels.

The i-th room (1 ≤ i ≤ n) has a_i illusion rate. To go from the x-th room to the y-th room, there must exist a tunnel between x and y, and it takes max(|a_x + a_y|, |a_x - a_y|) energy. |z| denotes the absolute value of z.

To prevent grave robbers, the maze can change the illusion rate of any room in it. Chanek and Indiana would ask q queries.

There are two types of queries to be done:

  * 1\ u\ c — The illusion rate of the x-th room is changed to c (1 ≤ u ≤ n, 0 ≤ |c| ≤ 10^9). 
  * 2\ u\ v — Chanek and Indiana ask you the minimum sum of energy needed to take the secret treasure at room v if they are initially at room u (1 ≤ u, v ≤ n). 



Help them, so you can get a portion of the treasure!

Input

The first line contains two integers n and q (2 ≤ n ≤ 10^5, 1 ≤ q ≤ 10^5) — the number of rooms in the maze and the number of queries.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ |a_i| ≤ 10^9) — inital illusion rate of each room.

The i-th of the next n-1 lines contains two integers s_i and t_i (1 ≤ s_i, t_i ≤ n), meaning there is a tunnel connecting s_i-th room and t_i-th room. The given edges form a tree.

The next q lines contain the query as described. The given queries are valid.

Output

For each type 2 query, output a line containing an integer — the minimum sum of energy needed for Chanek and Indiana to take the secret treasure.

Example

Input


6 4
10 -9 2 -1 4 -6
1 5
5 4
5 6
6 2
6 3
2 1 2
1 1 -3
2 1 2
2 3 3


Output


39
32
0

Note

<image>

In the first query, their movement from the 1-st to the 2-nd room is as follows.

  * 1 → 5 — takes max(|10 + 4|, |10 - 4|) = 14 energy. 
  * 5 → 6 — takes max(|4 + (-6)|, |4 - (-6)|) = 10 energy. 
  * 6 → 2 — takes max(|-6 + (-9)|, |-6 - (-9)|) = 15 energy. 

In total, it takes 39 energy.

In the second query, the illusion rate of the 1-st room changes from 10 to -3.

In the third query, their movement from the 1-st to the 2-nd room is as follows.

  * 1 → 5 — takes max(|-3 + 4|, |-3 - 4|) = 7 energy. 
  * 5 → 6 — takes max(|4 + (-6)|, |4 - (-6)|) = 10 energy. 
  * 6 → 2 — takes max(|-6 + (-9)|, |-6 - (-9)|) = 15 energy. 



Now, it takes 32 energy.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int max_n = 1e5 + 10, inf = 1000111222;
const int max_lev = 18;
class tree {
 public:
  int tin[max_n], tout[max_n];
  int h[max_n];
  int p[max_lev][max_n];
  void init(int n, vector<int> g[], int root = 0) {
    curt = -1;
    for (int i = 0; i < max_lev; ++i) {
      p[i][root] = root;
    }
    dfs(root, g);
    get_all_p(n);
  }
  bool is_ancestor(int u, int v) const {
    return tin[u] <= tin[v] && tout[u] >= tout[v];
  }
  bool is_on_path(int u, int v, int lca, int q) {
    return is_ancestor(lca, q) && (is_ancestor(q, u) || is_ancestor(q, v));
  }
  bool is_edge_on_path(int u, int v, int lca, int q1, int q2) {
    return is_on_path(u, v, lca, q1) && is_on_path(u, v, lca, q2);
  }
  int lca(int u, int v) const {
    if (is_ancestor(u, v)) {
      return u;
    }
    for (int i = max_lev - 1; i >= 0; --i) {
      if (!is_ancestor(p[i][u], v)) {
        u = p[i][u];
      }
    }
    return p[0][u];
  }
  int get_dist(int u, int v) const {
    const int lc = lca(u, v);
    return h[u] + h[v] - 2 * h[lc];
  }
  int get_up(int v, int dist) const {
    for (int i = max_lev - 1; i >= 0; --i) {
      if (get_bit(dist, i)) {
        v = p[i][v];
      }
    }
    return v;
  }

 protected:
  void dfs(int v, vector<int> g[]) {
    tin[v] = ++curt;
    for (int to : g[v]) {
      if (to == p[0][v]) {
        continue;
      }
      p[0][to] = v;
      h[to] = h[v] + 1;
      dfs(to, g);
    }
    tout[v] = curt;
  }
  void get_all_p(int n) {
    for (int lev = 1; lev < max_lev; ++lev) {
      for (int i = 0; i < n; ++i) {
        p[lev][i] = p[lev - 1][p[lev - 1][i]];
      }
    }
  }
  static bool get_bit(int mask, int pos) { return (mask >> pos) & 1; }
  int curt;
};
class heavy_light_tree : public tree {
 public:
  int up[max_n], sz[max_n];
  vector<int> order;
  void init(int n, vector<int> g[], int root = 0) {
    curt = -1;
    for (int i = 0; i < max_lev; ++i) {
      p[i][root] = root;
    }
    reorder_subtrees(root, -1, g);
    up[root] = root;
    dfs(root, g);
    get_all_p(n);
  }
  template <bool lca_inclusive, typename Callback>
  void decompose_on_paths(int v1, int v2, Callback &callback) const {
    const int lc = lca(v1, v2);
    vertical_decompose_on_paths<lca_inclusive>(v1, lc, callback);
    vertical_decompose_on_paths<false>(v2, lc, callback);
  }
  template <bool lca_inclusive>
  vector<pair<int, int>> decompose_on_paths(int v1, int v2) const {
    vector<pair<int, int>> res;
    auto callback = [&res](int l, int r) { res.emplace_back(l, r); };
    decompose_on_paths<lca_inclusive>(v1, v2, callback);
    return res;
  }
  vector<int> get_light_edges_down(int u, int v, int lca) const {
    vector<int> res;
    lol_kek(u, lca, res);
    lol_kek(v, lca, res);
    return res;
  }
  void lol_kek(int v, int parent, vector<int> &res) const {
    while (true) {
      if (is_ancestor(up[v], parent)) {
        return;
      }
      res.push_back(up[v]);
      v = p[0][up[v]];
    }
  }

 private:
  template <bool parent_inclusive, typename Callback>
  void vertical_decompose_on_paths(int v, int parent,
                                   Callback &callback) const {
    while (true) {
      if (is_ancestor(up[v], parent)) {
        const int l = tin[parent] + !parent_inclusive, r = tin[v];
        if (l <= r) {
          callback(l, r);
        }
        return;
      }
      callback(tin[up[v]], tin[v]);
      v = p[0][up[v]];
    }
  }
  void reorder_subtrees(int v, int p, vector<int> g[]) {
    sz[v] = 1;
    for (int i = 0; i < g[v].size(); ++i) {
      if (g[v][i] == p) {
        swap(g[v][i], g[v].back());
        g[v].pop_back();
        break;
      }
    }
    for (int to : g[v]) {
      reorder_subtrees(to, v, g);
      sz[v] += sz[to];
    }
    for (int i = 1; i < g[v].size(); ++i) {
      if (sz[g[v][i]] > sz[g[v][0]]) {
        swap(g[v][i], g[v][0]);
      }
    }
  }
  void dfs(int v, vector<int> g[]) {
    order.push_back(v);
    tin[v] = ++curt;
    sz[v] = 1;
    for (int to : g[v]) {
      if (to == p[0][v]) {
        continue;
      }
      up[to] = to;
      if (to == g[v][0]) {
        up[to] = up[v];
      }
      p[0][to] = v;
      h[to] = h[v] + 1;
      dfs(to, g);
      sz[v] += sz[to];
    }
    tout[v] = curt;
  }
};
vector<int> reb[max_n];
int a[max_n];
heavy_light_tree T;
const int magic = 300;
int type[max_n];
int A[max_n];
int B[max_n];
long long pref_value[max_n];
void dfs_push_value(int now) {
  for (auto wh : reb[now]) {
    pref_value[wh] += pref_value[now];
    dfs_push_value(wh);
  }
}
bool mark[max_n];
pair<bool, int> G[max_n];
int G_T;
bool get_G(int a) {
  if (G[a].second < G_T) {
    G[a].first = 0;
    G[a].second = G_T;
  }
  return G[a].first;
}
void set_G(int a, bool val) {
  if (G[a].second < G_T) {
    G[a].first = 0;
    G[a].second = G_T;
  }
  G[a].first = val;
}
int main() {
  int n, q;
  scanf("%d%d", &n, &q);
  for (int i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  for (int i = 1; i < n; i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    u--;
    v--;
    reb[u].push_back(v);
    reb[v].push_back(u);
  }
  T.init(n, reb, 0);
  for (int i = 0; i < q; i++) {
    scanf("%d%d%d", &type[i], &A[i], &B[i]);
    if (type[i] == 1) {
      A[i]--;
    } else {
      A[i]--;
      B[i]--;
    }
  }
  auto get_edge_w = [&](int a, int b) { return max(abs(a + b), abs(a - b)); };
  for (int i = 0; i < q; i += magic) {
    int L = i;
    int R = min(q, i + magic);
    memset(mark, 0, sizeof(mark));
    vector<int> cur_mark;
    for (int j = L; j < R; j++) {
      if (type[j] == 1) {
        mark[A[j]] = 1;
        cur_mark.push_back(A[j]);
      }
    }
    sort(cur_mark.begin(), cur_mark.end());
    cur_mark.resize(unique(cur_mark.begin(), cur_mark.end()) -
                    cur_mark.begin());
    memset(pref_value, 0, sizeof(pref_value));
    for (int i = 1; i < n; i++) {
      if (!mark[i] && !mark[T.p[0][i]]) {
        pref_value[i] = get_edge_w(a[i], a[T.p[0][i]]);
      }
    }
    dfs_push_value(0);
    for (int j = L; j < R; j++) {
      if (type[j] == 1) {
        a[A[j]] = B[j];
      } else {
        int u = A[j];
        int v = B[j];
        int lca = T.lca(u, v);
        long long ans = 0;
        ans += pref_value[u];
        ans += pref_value[v];
        ans -= 2 * pref_value[lca];
        G_T++;
        for (auto marked : cur_mark) {
          if (marked != 0 && (mark[marked] || mark[T.p[0][marked]]) &&
              get_G(marked) == 0 &&
              T.is_edge_on_path(u, v, lca, marked, T.p[0][marked])) {
            set_G(marked, 1);
            ans += get_edge_w(a[marked], a[T.p[0][marked]]);
          }
          if ((int)(reb[marked].size()) != 0) {
            marked = reb[marked][0];
            if (marked != 0 && (mark[marked] || mark[T.p[0][marked]]) &&
                get_G(marked) == 0 &&
                T.is_edge_on_path(u, v, lca, marked, T.p[0][marked])) {
              set_G(marked, 1);
              ans += get_edge_w(a[marked], a[T.p[0][marked]]);
            }
          }
        }
        auto lol = T.get_light_edges_down(u, v, lca);
        for (auto marked : lol) {
          if (marked != 0 && (mark[marked] || mark[T.p[0][marked]]) &&
              get_G(marked) == 0 &&
              T.is_edge_on_path(u, v, lca, marked, T.p[0][marked])) {
            set_G(marked, 1);
            ans += get_edge_w(a[marked], a[T.p[0][marked]]);
          }
        }
        cout << ans << "\n";
      }
    }
  }
}

```