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

Solution (in JAVA):

Solution:
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

class Main implements Runnable {
	public static void main(String[] args) {
		new Thread(null, new Main(), "", Runtime.getRuntime().maxMemory()).start();
	}

	public void run() {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int q = sc.nextInt();
		int[] w = new int[n];
		for (int i = 0; i < n; ++i) {
			w[i] = sc.nextInt();
		}
		HLDecomposition hl = new HLDecomposition(n);
		for (int i = 0; i < n - 1; ++i) {
			int s = sc.nextInt() - 1;
			int e = sc.nextInt() - 1;
			hl.ae(s, e);
		}
		hl.pre();
		SegmentTree st = new SegmentTree(n);
		for (int i = 0; i < n; ++i) {
			st.v[hl.id[i] + st.n - 1] = new E(w[i], 1);
		}
		for (int i = st.n - 2; i >= 0; --i) {
			st.v[i] = merge(st.v[2 * i + 1], st.v[2 * i + 2]);
		}
		while (q-- > 0) {
			int t = sc.nextInt();
			int a = sc.nextInt() - 1;
			int b = sc.nextInt() - 1;
			int c = sc.nextInt();
			if (t == 1) {// modification query
				modification(a, b, c, hl, st);
			} else {// output query
				pw.println(output(a, b, hl, st));
			}
		}
		pw.close();
	}

	long output(int a, int b, HLDecomposition hl, SegmentTree st) {
		E ea = new E(-(Long.MAX_VALUE >> 8), 1);
		E eb = new E(-(Long.MAX_VALUE >> 8), 1);

		while (hl.head[a] != hl.head[b]) {
			if (hl.depth[hl.head[a]] < hl.depth[hl.head[b]]) {
				int tmp = a;
				a = b;
				b = tmp;
				E tmp_e = new E(ea.top, ea.bottom, ea.max, ea.sum);
				ea = eb;
				eb = tmp_e;
			}
			// a???head???????????±???
			ea = merge(st.query(hl.id[hl.head[a]], hl.id[a] + 1), ea);
			a = hl.parent[hl.head[a]];
		}
		if (hl.depth[a] < hl.depth[b]) {
			int tmp = a;
			a = b;
			b = tmp;
			E tmp_e = new E(ea.top, ea.bottom, ea.max, ea.sum);
			ea = eb;
			eb = tmp_e;
		}
		// a???????????±???
		return merge(eb.reverse(), merge(st.query(hl.id[b], hl.id[a] + 1), ea)).max;
	}

	void modification(int a, int b, int c, HLDecomposition hl, SegmentTree st) {
		while (hl.head[a] != hl.head[b]) {
			if (hl.depth[hl.head[a]] < hl.depth[hl.head[b]]) {
				int tmp = a;
				a = b;
				b = tmp;
			}
			// a???head???????????±???
			st.modification(hl.id[hl.head[a]], hl.id[a] + 1, c);
			a = hl.parent[hl.head[a]];
		}
		if (hl.depth[a] < hl.depth[b]) {
			int tmp = a;
			a = b;
			b = tmp;
		}
		// a???????????±???
		if (hl.id[b] > hl.id[a]) {
			throw new AssertionError();
		}
		st.modification(hl.id[b], hl.id[a] + 1, c);
	}

	class E {
		long top;
		long bottom;
		long max;
		long sum;

		public E(long top, long bottom, long max, long sum) {
			this.top = top;
			this.bottom = bottom;
			this.max = max;
			this.sum = sum;
		}

		public E(long v, int width) {
			this.top = Math.max(v, v * width);
			this.bottom = Math.max(v, v * width);
			this.max = Math.max(v, v * width);
			this.sum = width * v;
		}

		public E() {
			this.top = -(Long.MAX_VALUE >> 8);
			this.bottom = -(Long.MAX_VALUE >> 8);
			this.max = -(Long.MAX_VALUE >> 8);
			this.sum = 0;
		}

		E reverse() {
			E e = new E();
			e.top = this.bottom;
			e.bottom = this.top;
			e.sum = this.sum;
			e.max = this.max;
			return e;
		}

		void tr() {
			System.out.println("top" + top);
			System.out.println("bottom" + bottom);
			System.out.println("max" + max);
			System.out.println("sum" + sum);
		}
	}

	E merge(E top, E bottom) {
		E e = new E();
		e.top = Math.max(top.top, top.sum + bottom.top);
		e.bottom = Math.max(bottom.bottom, top.bottom + bottom.sum);
		e.max = Math.max(Math.max(top.max, bottom.max), top.bottom + bottom.top);
		e.sum = top.sum + bottom.sum;
		return e;
	}

	class SegmentTree {
		int n;
		E[] v;
		long[] lazy;
		long nil = Long.MAX_VALUE >> 3;

		public SegmentTree(int n) {
			this.n = 1;
			while (this.n < n) {
				this.n *= 2;
			}
			v = new E[2 * this.n - 1];
			lazy = new long[2 * this.n - 1];
			Arrays.fill(lazy, nil);
			Arrays.fill(v, new E());
		}

		void push(int k, int l, int r) {
			if (lazy[k] == nil) {
				return;
			}
			v[k] = new E(lazy[k], r - l);
			if (r - l > 1) {
				lazy[2 * k + 1] = lazy[k];
				lazy[2 * k + 2] = lazy[k];
			}
			lazy[k] = nil;
		}

		void modification(int a, int b, int c) {
			modification(a, b, c, 0, n, 0);
		}

		// [a,b),[l,r)
		void modification(int a, int b, int c, int l, int r, int k) {
			push(k, l, r);
			if (b <= l || r <= a) {
				return;
			}
			if (a <= l && r <= b) {
				lazy[k] = c;
				push(k, l, r);
			} else {
				modification(a, b, c, l, (l + r) / 2, 2 * k + 1);
				modification(a, b, c, (l + r) / 2, r, 2 * k + 2);
				v[k] = merge(v[2 * k + 1], v[2 * k + 2]);
			}
		}

		E query(int a, int b) {
			return query(a, b, 0, n, 0);
		}

		E query(int a, int b, int l, int r, int k) {
			if (b <= l || r <= a) {
				return new E();
			}
			push(k, l, r);
			if (a <= l && r <= b) {
				return v[k];
			} else {
				E vl = query(a, b, l, (l + r) / 2, 2 * k + 1);
				E vr = query(a, b, (l + r) / 2, r, 2 * k + 2);
				return merge(vl, vr);
			}
		}
	}

	class HLDecomposition {
		int n;
		int[] depth;
		int[] head;
		int[] heavy;
		int[] parent;
		int[] sz;
		ArrayList<Integer>[] g;
		int[] id;

		@SuppressWarnings("unchecked")
		public HLDecomposition(int n) {
			this.n = n;
			depth = new int[n];
			head = new int[n];
			heavy = new int[n];
			parent = new int[n];
			id = new int[n];
			sz = new int[n];
			g = new ArrayList[n];
			for (int i = 0; i < n; ++i) {
				g[i] = new ArrayList<>();
			}
			Arrays.fill(head, -1);
			Arrays.fill(id, -1);
			Arrays.fill(parent, -1);
		}

		void ae(int a, int b) {
			g[a].add(b);
			g[b].add(a);
		}

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

		void bfs() {
			ArrayDeque<Integer> pend = new ArrayDeque<>();
			int gen = 0;
			pend.add(0);
			while (!pend.isEmpty()) {
				int v = pend.pollFirst();
				int top = v;
				for (; v != -1; v = heavy[v]) {
					id[v] = gen++;
					head[v] = top;
					for (int d : g[v]) {
						if (d == parent[v] || d == heavy[v]) {
							continue;
						}
						pend.add(d);
					}
				}
			}
		}

		int lca(int u, int v) {
			if (head[u] != head[v]) {
				if (depth[head[u]] < depth[head[v]]) {
					int tmp = u;
					u = v;
					v = tmp;
				}
				return lca(parent[head[u]], v);
			} else {
				if (depth[u] > depth[v]) {
					int tmp = u;
					u = v;
					v = tmp;
				}
				return u;
			}
		}

		int dfs(int c, int p) {
			parent[c] = p;
			int s = 1;
			int to = -1;
			for (int d : g[c]) {
				if (d == p)
					continue;
				depth[d] = depth[c] + 1;
				s += dfs(d, c);
				if (to == -1 || sz[d] > sz[to]) {
					to = d;
				}
			}
			sz[c] = s;
			heavy[c] = to;
			return s;
		}

	}

	static void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}

}