#include <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#include <iomanip>
#include <cassert>
#include <bitset>
#include <functional>
using namespace std;

typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(c) (c).begin(), (c).end()
#define uniq(c) c.erase(unique(all(c)), (c).end())
#define index(xs, x) (int)(lower_bound(all(xs), x) - xs.begin())
#define _1 first
#define _2 second
#define pb push_back
#define INF (1LL<<60)
#define MOD 1000000007

struct HLDecomposition {
  vector<vector<int> > G;
  vector<int> vid, head, heavy, parent, depth, inv;
  HLDecomposition(int n) :
    G(n), vid(n, -1), head(n), heavy(n, -1), parent(n), depth(n), inv(n) {}

  void add_edge(int x, int y) {
    G[x].pb(y);
    G[y].pb(x);
  }

  void build() {
    dfs(0, -1);
    bfs();
  }

  int dfs(int x, int p) {
    parent[x] = p;
    int sub = 1, max_sub = 0;
    for (int t : G[x]) {
      if (t == p) continue;
      depth[t] = depth[x]+1;
      int sub_t = dfs(t, x);
      sub += sub_t;
      if (max_sub < sub_t) max_sub = sub_t, heavy[x] = t;
    }
    return sub;
  }

  void bfs() {
    int k = 0;
    queue<int> q;
    q.push(0);
    while (!q.empty()) {
      int h = q.front(); q.pop();
      for (int i=h; i!=-1; i=heavy[i]) {
        vid[i] = k++;
        inv[vid[i]] = i;
        head[i] = h;
        for (int j : G[i]) {
          if (j == parent[i] || j == heavy[i]) continue;
          q.push(j);
        }
      }
    }
  }

  void for_each(int u, int v, function<void(int, int, int)> f) {
    if (vid[u] > vid[v]) {
      f(max(vid[head[u]], vid[v]), vid[u], 1);
      if (head[u] != head[v]) for_each(parent[head[u]], v, f);
    }
    else {
      if (head[u] != head[v]) for_each(u, parent[head[v]], f);
      f(max(vid[head[v]], vid[u]), vid[v], 0);
    }
  }
};

struct Node {
  long long l, r, m, sum;
  Node() : l(-INF), r(-INF), m(-INF), sum(-INF) {}
  Node(long long l, long long r, long long m, long long s) :
    l(l), r(r), m(m), sum(s) {}
};
Node op(Node a, Node b) {
  if (a.m == -INF) return b;
  if (b.m == -INF) return a;
  return Node(
    max(a.l, a.sum + b.l),
    max(b.r, b.sum + a.r),
    max({a.m, b.m, a.r + b.l}),
    a.sum + b.sum
  );
}

#define MAX_N (1<<18)
Node seg[MAX_N*2-1];
long long lazy[MAX_N*2-1];

void setLazy(int k, int v, int size) {
  lazy[k] = v;
  long long u = v;
  if (v >= 0) u = 1LL*size*v;
  seg[k] = Node(u, u, u, 1LL*size*v);
}

void push(int k, int size) {
  if (lazy[k] == -INF) return;
  setLazy(k*2+1, lazy[k], size/2);
  setLazy(k*2+2, lazy[k], size/2);
  lazy[k] = -INF;
}

Node query(int a, int b, int k=0, int l=0, int r=MAX_N) {
  if (r <= a || b <= l) return Node();
  if (a <= l && r <= b) return seg[k];
  push(k, r-l);
  return op(
    query(a, b, k*2+1, l, (l+r)/2),
    query(a, b, k*2+2, (l+r)/2, r));
}

void fill(int a, int b, int val, int k=0, int l=0, int r=MAX_N) {
  if (r <= a || b <= l) return;
  if (a <= l && r <= b) {
    setLazy(k, val, r-l);
    return;
  }
  push(k, r-l);
  fill(a, b, val, k*2+1, l, (l+r)/2);
  fill(a, b, val, k*2+2, (l+r)/2, r);
  seg[k] = op(seg[k*2+1], seg[k*2+2]);
}

int N, Q;
int W[200000];

signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  cin >> N >> Q;
  HLDecomposition hld(N);
  rep(i, MAX_N*2-1) lazy[i] = -1;
  rep(i, N) cin >> W[i];
  rep(i, N-1) {
    int u, v;
    cin >> u >> v;
    u--, v--;
    hld.add_edge(u, v);
  }
  hld.build();
  rep(i, N) {
    hld.for_each(i, i, [&](int l, int r, int d) {
      fill(l, r+1, W[i]);
    });
  }

  rep(_, Q) {
    int t, x, y, z;
    cin >> t >> x >> y >> z;
    x--, y--;
    if (t == 1) {
      // update [x, y] -> z
      hld.for_each(x, y, [&](int l, int r, int d) {
        fill(l, r+1, z);
      });
    }
    else {
      // query [x, y]
      Node node;
      hld.for_each(x, y, [&](int l, int r, int d) {
        Node t = query(l, r+1);
        if (d == 1) swap(t.l, t.r);
        node = op(node, t);
      });
      cout << node.m << "\n";
    }
  }
  return 0;
}
### Prompt

Please formulate a CPP solution to the following problem:

Given a tree with n (1 ≤ n ≤ 200,000) nodes and a list of q (1 ≤ q ≤ 100,000) queries, process the queries in order and output a value for each output query. The given tree is connected and each node on the tree has a weight wi (-10,000 ≤ wi ≤ 10,000).

Each query consists of a number ti (ti = 1, 2), which indicates the type of the query , and three numbers ai, bi and ci (1 ≤ ai, bi ≤ n, -10,000 ≤ ci ≤ 10,000). Depending on the query type, process one of the followings:

* (ti = 1: modification query) Change the weights of all nodes on the shortest path between ai and bi (both inclusive) to ci.

* (ti = 2: output query) First, create a list of weights on the shortest path between ai and bi (both inclusive) in order. After that, output the maximum sum of a non-empty continuous subsequence of the weights on the list. ci is ignored for output queries.



Input

The first line contains two integers n and q. On the second line, there are n integers which indicate w1, w2, ... , wn.

Each of the following n - 1 lines consists of two integers si and ei (1 ≤ si, ei ≤ n), which means that there is an edge between si and ei.

Finally the following q lines give the list of queries, each of which contains four integers in the format described above. Queries must be processed one by one from top to bottom.

Output

For each output query, output the maximum sum in one line.

Examples

Input

3 4
1 2 3
1 2
2 3
2 1 3 0
1 2 2 -4
2 1 3 0
2 2 2 0


Output

6
3
-4


Input

7 5
-8 5 5 5 5 5 5
1 2
2 3
1 4
4 5
1 6
6 7
2 3 7 0
2 5 2 0
2 4 3 0
1 1 1 -1
2 3 7 0


Output

12
10
10
19


Input

21 30
10 0 -10 -8 5 -5 -4 -3 1 -2 8 -1 -7 2 7 6 -9 -6 3 4 9
10 3
3 2
3 12
12 4
4 13
4 9
10 21
21 1
1 11
11 14
1 15
10 6
6 17
6 16
6 5
5 18
5 19
10 7
10 8
8 20
1 1 21 -10
1 3 19 10
2 1 13 0
1 4 18 8
1 5 17 -5
2 16 7 0
1 6 16 5
1 7 15 4
2 4 20 0
1 8 14 3
1 9 13 -1
2 9 18 0
1 10 12 2
1 11 11 -8
2 21 15 0
1 12 10 1
1 13 9 7
2 6 14 0
1 14 8 -2
1 15 7 -7
2 10 2 0
1 16 6 -6
1 17 5 9
2 12 17 0
1 18 4 6
1 19 3 -3
2 11 8 0
1 20 2 -4
1 21 1 -9
2 5 19 0


Output

20
9
29
27
10
12
1
18
-2
-3

### Response

```cpp
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#include <iomanip>
#include <cassert>
#include <bitset>
#include <functional>
using namespace std;

typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(c) (c).begin(), (c).end()
#define uniq(c) c.erase(unique(all(c)), (c).end())
#define index(xs, x) (int)(lower_bound(all(xs), x) - xs.begin())
#define _1 first
#define _2 second
#define pb push_back
#define INF (1LL<<60)
#define MOD 1000000007

struct HLDecomposition {
  vector<vector<int> > G;
  vector<int> vid, head, heavy, parent, depth, inv;
  HLDecomposition(int n) :
    G(n), vid(n, -1), head(n), heavy(n, -1), parent(n), depth(n), inv(n) {}

  void add_edge(int x, int y) {
    G[x].pb(y);
    G[y].pb(x);
  }

  void build() {
    dfs(0, -1);
    bfs();
  }

  int dfs(int x, int p) {
    parent[x] = p;
    int sub = 1, max_sub = 0;
    for (int t : G[x]) {
      if (t == p) continue;
      depth[t] = depth[x]+1;
      int sub_t = dfs(t, x);
      sub += sub_t;
      if (max_sub < sub_t) max_sub = sub_t, heavy[x] = t;
    }
    return sub;
  }

  void bfs() {
    int k = 0;
    queue<int> q;
    q.push(0);
    while (!q.empty()) {
      int h = q.front(); q.pop();
      for (int i=h; i!=-1; i=heavy[i]) {
        vid[i] = k++;
        inv[vid[i]] = i;
        head[i] = h;
        for (int j : G[i]) {
          if (j == parent[i] || j == heavy[i]) continue;
          q.push(j);
        }
      }
    }
  }

  void for_each(int u, int v, function<void(int, int, int)> f) {
    if (vid[u] > vid[v]) {
      f(max(vid[head[u]], vid[v]), vid[u], 1);
      if (head[u] != head[v]) for_each(parent[head[u]], v, f);
    }
    else {
      if (head[u] != head[v]) for_each(u, parent[head[v]], f);
      f(max(vid[head[v]], vid[u]), vid[v], 0);
    }
  }
};

struct Node {
  long long l, r, m, sum;
  Node() : l(-INF), r(-INF), m(-INF), sum(-INF) {}
  Node(long long l, long long r, long long m, long long s) :
    l(l), r(r), m(m), sum(s) {}
};
Node op(Node a, Node b) {
  if (a.m == -INF) return b;
  if (b.m == -INF) return a;
  return Node(
    max(a.l, a.sum + b.l),
    max(b.r, b.sum + a.r),
    max({a.m, b.m, a.r + b.l}),
    a.sum + b.sum
  );
}

#define MAX_N (1<<18)
Node seg[MAX_N*2-1];
long long lazy[MAX_N*2-1];

void setLazy(int k, int v, int size) {
  lazy[k] = v;
  long long u = v;
  if (v >= 0) u = 1LL*size*v;
  seg[k] = Node(u, u, u, 1LL*size*v);
}

void push(int k, int size) {
  if (lazy[k] == -INF) return;
  setLazy(k*2+1, lazy[k], size/2);
  setLazy(k*2+2, lazy[k], size/2);
  lazy[k] = -INF;
}

Node query(int a, int b, int k=0, int l=0, int r=MAX_N) {
  if (r <= a || b <= l) return Node();
  if (a <= l && r <= b) return seg[k];
  push(k, r-l);
  return op(
    query(a, b, k*2+1, l, (l+r)/2),
    query(a, b, k*2+2, (l+r)/2, r));
}

void fill(int a, int b, int val, int k=0, int l=0, int r=MAX_N) {
  if (r <= a || b <= l) return;
  if (a <= l && r <= b) {
    setLazy(k, val, r-l);
    return;
  }
  push(k, r-l);
  fill(a, b, val, k*2+1, l, (l+r)/2);
  fill(a, b, val, k*2+2, (l+r)/2, r);
  seg[k] = op(seg[k*2+1], seg[k*2+2]);
}

int N, Q;
int W[200000];

signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  cin >> N >> Q;
  HLDecomposition hld(N);
  rep(i, MAX_N*2-1) lazy[i] = -1;
  rep(i, N) cin >> W[i];
  rep(i, N-1) {
    int u, v;
    cin >> u >> v;
    u--, v--;
    hld.add_edge(u, v);
  }
  hld.build();
  rep(i, N) {
    hld.for_each(i, i, [&](int l, int r, int d) {
      fill(l, r+1, W[i]);
    });
  }

  rep(_, Q) {
    int t, x, y, z;
    cin >> t >> x >> y >> z;
    x--, y--;
    if (t == 1) {
      // update [x, y] -> z
      hld.for_each(x, y, [&](int l, int r, int d) {
        fill(l, r+1, z);
      });
    }
    else {
      // query [x, y]
      Node node;
      hld.for_each(x, y, [&](int l, int r, int d) {
        Node t = query(l, r+1);
        if (d == 1) swap(t.l, t.r);
        node = op(node, t);
      });
      cout << node.m << "\n";
    }
  }
  return 0;
}
```