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;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,"Line:",__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
	return os<<vc<t>(all(a));
}

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

void print(ll x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}
void possible(bool ex=true){
	#ifdef CAPITAL
	cout<<"POSSIBLE"<<endl;
	#else
	cout<<"Possible"<<endl;
	#endif
	if(ex)exit(0);
}
void impossible(bool ex=true){
	#ifdef CAPITAL
	cout<<"IMPOSSIBLE"<<endl;
	#else
	cout<<"Impossible"<<endl;
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
int mask(int i){
	return (int(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
    static random_device rd;
    static mt19937_64 gen(rd());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}

template<class t>
int lwb(const vc<t>&v,const t&a){
	return lower_bound(all(v),a)-v.bg;
}

//cf16-tournament-round1-open A
//JOISC2013 day4 Spaceships
template<class N>
struct linkcut{
	struct Node{
		using np=Node*;
		np l,r,p;
		bool rev;
		N x;
		Node():l(0),r(0),p(0),rev(false),x(){}
		void reverse(){
			rev^=true;
			x.reverse();
		}
		void propagate(){
			if(rev){
				swap(l,r);
				if(l)l->reverse();
				if(r)r->reverse();
				rev=false;
			}
			if(l)x.push(l->x);
			if(r)x.push(r->x);
			x.clear();
		}
		void update(){
			x.single();
			if(l)
				x.updatel(l->x);
			if(r)
				x.updater(r->x);
		}
		int pos(){
			if(p&&p->l==this) return -1;
			if(p&&p->r==this) return 1;
			return 0;
		}
		void prepare(){
			if(pos())
				p->prepare();
			propagate();
		}
		void rotate(){
			np q=p,c;
			if(pos()==1){
				c=l;
				l=p;
				p->r=c;
			}else{
				c=r;
				r=p;
				p->l=c;
			}
			if(c)c->p=p;
			p=p->p;
			q->p=this;
			if(p&&p->l==q)p->l=this;
			if(p&&p->r==q)p->r=this;
			q->update();
		}
		void splay(){
			prepare();
			while(pos()){
				int a=pos(),b=p->pos();
				if(b&&a==b)p->rotate();
				if(b&&a!=b)rotate();
				rotate();
			}
			update();
		}
		void expose(){
			for(np a=this;a;a=a->p)a->splay();
			for(np a=this;a->p;a=a->p){
				a->p->r=a;
				a->p->update();
			}
			splay();
		}
		void evert(){
			expose();
			if(l){
				l->reverse();
				l=0;
				update();
			}
		}
		void link(np a){
			evert();
			p=a;
		}
		void cutchild(){
			expose();
			r=0;
			update();
		}
		void cutpar() {
			expose();
			assert(l);
			l->p=0;
			l=0;
			update();
		}
	}*x;
	linkcut(int n){
		x=new Node[n];
	}
	~linkcut(){delete[] x;}
	
	using np=typename Node::np;
	int lca(int aa,int bb){
		np a=x+aa,b=x+bb;
		a->expose();
		b->expose();
		if(!a->p)return -1;
		
		np d=a;
		while(a->p!=b){
			if(a->pos()==0)
				d=a->p;
			a=a->p;
		}
		if(a==b->l)return d-x;
		else return b-x;
	}
	void link(int a,int b){
		x[a].link(x+b);
	}
	void cutpar(int a){
		x[a].cutpar();
	}
	void expose(int a){
		x[a].expose();
	}
	void expose_path(int a,int b){
		x[a].evert();
		x[b].cutchild();
	}
	N&operator[](int i){
		return x[i].x;
	}
};
//N::reverse
//N::push
//N::clear
//N::single
//N::updatel,updater

//Do use segment tree
struct M{
	int l,r,s,m,c;
	void init(int v,int len){
		assert(len>=0);
		s=v*len;
		l=r=m=max(s,v);
		c=len;
	}
	void lazy(int v){
		init(v,c);
	}
	void reverse(){
		swap(l,r);
	}
};

M merge(M a,M b){
	if(a.c==0)return b;
	if(b.c==0)return a;
	int l=max(a.l,a.s+b.l);
	int r=max(a.r+b.s,b.r);
	int s=a.s+b.s;
	int m=max({a.m,a.r+b.l,b.m});
	return {l,r,s,m,a.c+b.c};
}

const int none=INT_MIN;

struct N{
	int v,lz;
	M m;
	void init(int a){
		v=a;
		lz=none;
		single();
	}
	void reverse(){
		m.reverse();
	}
	void lazy(int a){
		v=a;
		lz=a;
		m.lazy(a);
	}
	void push(N&x){
		if(lz!=none)
			x.lazy(lz);
	}
	void clear(){
		lz=none;
	}
	void single(){
		assert(lz==none);
		m.init(v,1);
	}
	void updatel(const N&x){
		assert(lz==none);
		m=merge(x.m,m);
	}
	void updater(const N&x){
		assert(lz==none);
		m=merge(m,x.m);
	}
	int getans(){
		return m.m;
	}
};

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	int n,q;cin>>n>>q;
	linkcut<N> t(n);
	rep(i,n){
		int w;cin>>w;
		t[i].init(w);
	}
	rep(_,n-1){
		int a,b;cin>>a>>b;
		a--;b--;
		t.link(a,b);
	}
	rep(_,q){
		int k,a,b,c;cin>>k>>a>>b>>c;
		a--;b--;
		t.expose_path(a,b);
		if(k==1)
			t[b].lazy(c);
		else
			print(t[b].getans());
	}
}