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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#define dump(...) cout<<"# "<<#__VA_ARGS__<<'='<<(__VA_ARGS__)<<endl
#define repi(i,a,b) for(int i=int(a);i<int(b);i++)
#define peri(i,a,b) for(int i=int(b);i-->int(a);)
#define rep(i,n) repi(i,0,n)
#define per(i,n) peri(i,0,n)
#define all(c) begin(c),end(c)
#define mp make_pair
#define mt make_tuple

typedef unsigned int uint;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<string> vs;

constexpr ll INF=1e18;
constexpr int MOD=1e9+7;
constexpr double EPS=1e-9;

template<typename T1,typename T2>
ostream& operator<<(ostream& os,const pair<T1,T2>& p){
	return os<<'('<<p.first<<','<<p.second<<')';
}
template<typename Ostream,typename Container>
Ostream& operator<<(Ostream& os,const Container& c){
	os<<'[';
	for(auto i=begin(c);i!=end(c);++i)
		os<<(i==begin(c)?"":" ")<<*i;
	return os<<']';
}

struct Edge{
	int src,dst;
	Edge(){}
	Edge(int s,int d):src(s),dst(d){}
};
typedef vector<vector<Edge>> Graph;

//int DFS1(const Graph& g,int p,int u,vi& sizes)
//{
//	for(auto e:g[u]) if(e.dst!=p)
//		sizes[u]+=DFS1(g,u,e.dst,sizes);
//	return sizes[u];
//}
//void DFS2(const Graph& g,int p,int u,const vi& sizes,vi& path,vvi& paths)
//{
//	path.push_back(u);
//	for(auto e:g[u]){
//		int v=e.dst;
//		if(v==p) continue;
//		if(sizes[v]*2>=sizes[u])
//			DFS2(g,u,v,sizes,path,paths);
//		else{
//			vi tmp;
//			DFS2(g,u,v,sizes,tmp,paths);
//		}
//	}
//	if(path[0]==u)
//		paths.push_back(path);
//}
vvi HeavyLightDecomposition(const Graph& g,int root=0)
{
	int n=g.size();
	vi sizes(n,1);
	//DFS1(g,-1,root,sizes);
	{
		stack<pii> st; st.emplace(-1,root);
		vi vis(n);
		while(st.size()){
			int p,u; tie(p,u)=st.top();
			if(!vis[u]){
				vis[u]=1;
				for(auto e:g[u]) if(e.dst!=p)
					st.emplace(u,e.dst);
			}
			else{
				for(auto e:g[u]) if(e.dst!=p)
					sizes[u]+=sizes[e.dst];
				st.pop();
			}
		}
	}
	//vi path;
	//vvi paths;
	//DFS2(g,-1,root,sizes,path,paths);
	vvi paths(1);
	{
		stack<tuple<int,int,int>> st; st.emplace(-1,root,0);
		vi vis(n);
		while(st.size()){
			int p,u,i; tie(p,u,i)=st.top();
			if(!vis[u]){
				paths[i].push_back(u);
				for(auto e:g[u]) if(e.dst!=p){
					if(sizes[e.dst]*2>=sizes[u])
						st.emplace(u,e.dst,i);
					else{
						paths.push_back(vi());
						st.emplace(u,e.dst,paths.size()-1);
					}
				}
				vis[u]=1;
			}
			else{
				st.pop();
			}
		}
	}
	return paths;
}

vi GetParents(const Graph& g,int root=0)
{
	vi ps(g.size(),-1);
	queue<int> q; q.push(root);
	while(q.size()){
		int u=q.front(); q.pop();
		for(auto e:g[u]) if(e.dst!=ps[u]){
			ps[e.dst]=u;
			q.push(e.dst);
		}
	}
	return ps;
}

struct LCA{
	vi ds;
	vvi ps;
	LCA(const Graph& g,int root=0):ds(g.size()),ps(32-__builtin_clz(g.size()),vi(g.size(),-1)){
		//DFS(g,-1,root,0);
		{
			stack<tuple<int,int,int>> st; st.emplace(-1,root,0);
			while(st.size()){
				int p,v,d; tie(p,v,d)=st.top(); st.pop();
				ds[v]=d;
				ps[0][v]=p;
				for(auto e:g[v]) if(e.dst!=p)
					st.emplace(v,e.dst,d+1);
			}
		}
		rep(i,ps.size()-1) rep(j,ps[i].size())
			ps[i+1][j]=ps[i][j]==-1?-1:ps[i][ps[i][j]];
	}
	//void DFS(const Graph& g,int p,int v,int d){
	//	ds[v]=d;
	//	ps[0][v]=p;
	//	for(auto e:g[v]) if(e.dst!=p)
	//		DFS(g,e.src,e.dst,d+1);
	//}
	int Find(int u,int v){
		if(ds[u]>ds[v]) swap(u,v);
		rep(i,ps.size())
			if((ds[v]-ds[u])>>i&1)
				v=ps[i][v];
		if(u==v) return u;
		per(i,ps.size())
			if(ps[i][u]!=ps[i][v])
				u=ps[i][u],v=ps[i][v];
		return ps[0][u];
	}
};

int NextPow2(int x)
{
	x--;
	for(int i=1;i<32;i*=2) x|=x>>i;
	return x+1;
}

struct SegmentTree{
	int size;
	vl sums,maxs,lmaxs,rmaxs,props;
	vi flags;
	SegmentTree(int n)
		:size(NextPow2(n)),sums(size*2),maxs(size*2,-INF),
		 lmaxs(size*2,-INF),rmaxs(size*2,-INF),props(size*2),flags(size*2){}
	void Update(int ql,int qr,ll x){Update(ql,qr,x,1,0,size);}
	tuple<ll,ll,ll,ll> Query(int ql,int qr){return Query(ql,qr,1,0,size);}
	
	void Propagate(int i,int l,int r){
		if(!flags[i]) return;
		flags[i]=0;
		sums[i]=(r-l)*(props[i]);
		maxs[i]=lmaxs[i]=rmaxs[i]=max(sums[i],props[i]);
		if(i<size){
			props[i*2]=props[i*2+1]=props[i];
			flags[i*2]=flags[i*2+1]=1;
		}
	}
	void Update(int ql,int qr,ll x,int i,int l,int r){
		Propagate(i,l,r);
		if(qr<=l || r<=ql) return;
		if(ql<=l && r<=qr){
			props[i]=x;
			flags[i]=1;
			Propagate(i,l,r);
			return;
		}
		Update(ql,qr,x,i*2,l,(l+r)/2);
		Update(ql,qr,x,i*2+1,(l+r)/2,r);
		sums[i]=sums[i*2]+sums[i*2+1];
		maxs[i]=max({maxs[i*2],maxs[i*2+1],rmaxs[i*2]+lmaxs[i*2+1]});
		lmaxs[i]=max(lmaxs[i*2],sums[i*2]+lmaxs[i*2+1]);
		rmaxs[i]=max(rmaxs[i*2+1],rmaxs[i*2]+sums[i*2+1]);
	}
	tuple<ll,ll,ll,ll> Query(int ql,int qr,int i,int l,int r){
		Propagate(i,l,r);
		if(qr<=l || r<=ql) return mt(0,-INF,-INF,-INF);
		if(ql<=l && r<=qr) return mt(sums[i],maxs[i],lmaxs[i],rmaxs[i]);
		ll s1,m1,l1,r1; tie(s1,m1,l1,r1)=Query(ql,qr,i*2,l,(l+r)/2);
		ll s2,m2,l2,r2; tie(s2,m2,l2,r2)=Query(ql,qr,i*2+1,(l+r)/2,r);
		return mt(s1+s2,max({m1,m2,r1+l2}),max(l1,s1+l2),max(r2,r1+s2));
	}
};

int main()
{
	#ifndef _GLIBCXX_DEBUG
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);
	constexpr char endl='\n';
	#endif
	
	for(int n,q;cin>>n>>q && n|q;){
		vi ws(n);
		rep(i,n) cin>>ws[i];
		Graph g(n);
		rep(i,n-1){
			int u,v; cin>>u>>v; u--,v--;
			g[u].emplace_back(u,v);
			g[v].emplace_back(v,u);
		}
		
		vvi paths=HeavyLightDecomposition(g);
		vi parents=GetParents(g);
		vi is(n),js(n);
		rep(i,paths.size()) rep(j,paths[i].size())
			is[paths[i][j]]=i,js[paths[i][j]]=j;
		
		vector<SegmentTree> sts;
		for(const auto& path:paths){
			int size=path.size();
			SegmentTree st(size);
			rep(i,size) st.Update(i,i+1,ws[path[i]]);
			sts.push_back(st);
		}
		
		LCA lca(g);
		
		rep(_,q){
			int t,u,v,x; cin>>t>>u>>v>>x; u--,v--;
			int a=lca.Find(u,v);
			if(t==1){ // update
				for(;;){
					int left=is[u]==is[a]?js[a]:0;
					sts[is[u]].Update(left,js[u]+1,x);
					if(is[u]==is[a]) break;
					else u=parents[paths[is[u]][0]];
				}
				for(;;){
					int left=is[v]==is[a]?js[a]+1:0;
					sts[is[v]].Update(left,js[v]+1,x);
					if(is[v]==is[a]) break;
					else v=parents[paths[is[v]][0]];
				}
			}
			else{ // query
				ll m1=-INF,l1=-INF;
				for(;;){
					int left=is[u]==is[a]?js[a]:0;
					ll s,m,l,r; tie(s,m,l,r)=sts[is[u]].Query(left,js[u]+1);
					tie(m1,l1)=mt(max({m,m1,r+l1}),max(l,s+l1));
					if(is[u]==is[a]) break;
					else u=parents[paths[is[u]][0]];
				}
				ll m2=-INF,l2=-INF;
				for(;;){
					int left=is[v]==is[a]?js[a]+1:0;
					ll s,m,l,r; tie(s,m,l,r)=sts[is[v]].Query(left,js[v]+1);
					tie(m2,l2)=mt(max({m,m2,r+l2}),max(l,s+l2));
					if(is[v]==is[a]) break;
					else v=parents[paths[is[v]][0]];
				}
				cout<<max({m1,m2,l1+l2})<<endl;
			}
		}
	}
}