#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ll __int128
const int N=1e5+5,inf=1e18;
struct gj{
    signed a;int b;
    friend gj operator+(gj a,gj b){
        gj c={a.a+b.a,a.b+b.b};
        while(c.b>inf)c.a++,c.b-=inf;
        while(c.b<0)c.a--,c.b+=inf;
        return c;
    }
    friend gj operator-(gj a,gj b){
        gj c={a.a-b.a,a.b-b.b};
        while(c.b>inf)c.a++,c.b-=inf;
        while(c.b<0)c.a--,c.b+=inf;
        return c;
    }
    ll gets(){
        return (ll)a*inf+b;
    }
}emps;
struct msg{
    signed sm;
    int rs;
    gj pf;
    friend msg operator+(msg a,msg b){
        return {a.sm+b.sm,a.rs+b.rs,a.pf+b.pf};
    }
    friend msg operator-(msg a,msg b){
        return {a.sm-b.sm,a.rs-b.rs,a.pf-b.pf};
    }
    msg rev(){
        return {-sm,-rs,emps-pf};
    }
}emp;
namespace trr{
    struct node{
        signed son[2],val;
        char fl;
        msg sm;
    }p[N*150];
    int bk[150*N],idx;
    int nw(){
        int y=bk[idx--];
        p[y].fl=30;
        return y;
    }
    void add(int x,int d,msg sm){
        if(p[x].fl<0){
            p[x].sm=p[x].sm+sm;
            return;
        }
        int c=d>>p[x].fl&1;
       // cout<<d<<"-"<<(int)p[x].fl<<" "<<c<<" "<<p[x].son[c]<<endl;
        if(!p[x].son[c])p[x].son[c]=nw(),p[p[x].son[c]].val=d,p[p[x].son[c]].fl=-1;
        else{
        //    cout<<d<<" "<<(int)p[p[x].son[c]].fl<<" "<<p[p[x].son[c]].val<<endl;
            if((d>>p[p[x].son[c]].fl+1)!=p[p[x].son[c]].val){
                for(int i=p[x].fl-1;;i--){
                    if((d>>i+1)!=p[p[x].son[c]].val>>i-p[p[x].son[c]].fl){
                        i++;
                        int t=p[x].son[c];
                    //    cout<<x<<" "<<i<<" "<<d<<" "<<p[x].son[c]<<" "<<p[p[x].son[c]].val<<" "<<(int)p[p[x].son[c]].fl<<" "<<(p[t].val>>p[x].fl-p[t].fl-1&1)<<endl;
                        p[x].son[c]=nw();
                        p[p[x].son[c]].val=d>>i+1;
                        p[p[x].son[c]].fl=i;
                        p[p[x].son[c]].son[p[t].val>>i-p[t].fl-1&1]=t;
                        break;
                    }
                }
            }
        }
        add(p[x].son[c],d,sm);
        p[x].sm=p[p[x].son[0]].sm+p[p[x].son[1]].sm;
    }
    msg gets(int x,int d){
        if(!x)return emp;
        if(p[x].fl<0)return p[x].sm;
        int c=d>>p[x].fl&1;
       // cout<<x<<" "<<(int)p[x].fl<<" "<<p[x].val<<" "<<p[x].son[0]<<" "<<p[x].son[1]<<" "<<(int)p[p[x].son[0]].fl<<" "<<p[p[x].son[0]].val<<" "<<(int)p[p[x].son[1]].fl<<" "<<p[p[x].son[1]].val<<" "<<c<<endl;
        if((d>>p[x].fl+1)>p[x].val)return p[x].sm;
        msg res=emp;
        if(c)res=res+p[p[x].son[0]].sm;
        if(p[p[x].son[c]].val<=(d>>p[p[x].son[c]].fl+1))res=res+gets(p[x].son[c],d);
        return res;
    }
    void add(int x,int l,int r,msg sm){
        add(x,l,sm);add(x,r+1,sm.rev());
    }
}
namespace tr{
    struct node{
        signed lson,rson,rt;
    }p[100*N];
    int idx;
    void init(int x,int op){
        if(!p[x].lson&&op==0)p[x].lson=++idx,p[idx].rt=trr::nw();
        if(!p[x].rson&&op==1)p[x].rson=++idx,p[idx].rt=trr::nw();
    }
    void add(int x,int d,int l,int r,int sm,int nl=0,int nr=1e9){
        if(sm>0)trr::add(p[x].rt,l,r,{sm,sm*d,{0,sm*d*d}});
        else trr::add(p[x].rt,l,r,{sm,sm*d,{-1,inf+sm*d*d}});
      //  cout<<x<<" "<<nl<<"-"<<nr<<" "<<p[x].rt<<" "<<p[x].lson<<endl;
        if(nl==nr)return;
        int mid=nl+nr>>1;
        if(d<=mid)init(x,0);
        else init(x,1);
        if(d<=mid)add(p[x].lson,d,l,r,sm,nl,mid);
        else add(p[x].rson,d,l,r,sm,mid+1,nr);
    }
    msg gets(int x,int l,int r,int d,int nl=0,int nr=1e9){
        if(!x||!d)return emp;
       // cout<<"ok"<<endl;
        if(l<=nl&&r>=nr)return trr::gets(p[x].rt,d);
        int mid=nl+nr>>1;
        if(r<=mid)return gets(p[x].lson,l,r,d,nl,mid);
        if(l>mid)return gets(p[x].rson,l,r,d,mid+1,nr);
        return gets(p[x].lson,l,r,d,nl,mid)+gets(p[x].rson,l,r,d,mid+1,nr);
    }
    int solve(int x,int x1,int x2,int x3,int x4,int k,int he,int sz,int nl=0,int nr=1e9){
        if(nl==nr)return nl;
        int mid=nl+nr>>1;
        msg c=trr::gets(p[p[x].rson].rt,x1)+trr::gets(p[p[x].rson].rt,x2)-trr::gets(p[p[x].rson].rt,x3)-trr::gets(p[p[x].rson].rt,x4);
        int ans=c.rs+he-mid*(c.sm+sz);
       // cout<<nl<<" "<<nr<<" "<<mid<<" "<<c.sm<<" "<<c.rs<<" "<<ans<<" "<<trr::gets(p[p[x].rson].rt,x2).rs<<endl;
        if(ans<=k)return solve(p[x].lson,x1,x2,x3,x4,k,he+c.rs,sz+c.sm,nl,mid);
        return solve(p[x].rson,x1,x2,x3,x4,k,he,sz,mid+1,nr);
    }
}
int n,m,w[N],fa[N],dep[N],mk[N],dfn[N],eds[N],idx,fs[N][20];
ll al;
vector<int>p[N];
void dfs(int x){
    mk[x]=1;dfn[x]=++idx;
    for(int i=1;i<=18;i++)fs[x][i]=fs[fs[x][i-1]][i-1];
    for(auto c:p[x]){
        if(mk[c])continue;
        dep[c]=dep[x]+1;
        fs[c][0]=x;
        dfs(c);
        fa[c]=x;
    }
    mk[x]=0;eds[x]=idx;
}
int up(int x,int k){
    while(k){
        x=fs[x][__lg(k&-k)];
        k^=k&-k;
    }
    return x;
}
int lca(int a,int b){
    if(dep[a]>dep[b])swap(a,b);
    b=up(b,dep[b]-dep[a]);
    if(a==b)return a;
    for(int i=18;i>=0;i--){
        if(fs[a][i]!=fs[b][i])a=fs[a][i],b=fs[b][i];
    }
    return fs[a][0];
}
msg gets(int x,int l=0,int r=1e9){
    return tr::gets(1,l,r,dfn[x]);
}
void print(ll x){
    if(x>9)print(x/10);
    putchar(x%10+'0');
}
signed main(){
    for(int i=1;i<150*N;i++)trr::bk[++trr::idx]=i;
    //fin();fout();
    cin>>n>>m;
    for(int i=1;i<n;i++){
        int x=i,y=i+1;
        cin>>x>>y;
        p[x].push_back(y);
        p[y].push_back(x);
    }
    tr::idx=1;
    tr::p[1].rt=trr::nw();
    dfs(1);
    for(int i=1;i<=n;i++)cin>>w[i],tr::add(1,w[i],dfn[i],eds[i],1),al+=w[i]*w[i];
    cout<<gets(2).sm<<endl;
    while(m--){
        int op=1,x=rand()%n+1,y=rand()%n+1,k;
        cin>>op>>x>>y;
        if(op==1){
            tr::add(1,w[x],dfn[x],eds[x],-1);
            al-=w[x]*w[x];
            w[x]=y;
            al+=y*y;
            tr::add(1,y,dfn[x],eds[x],1);
        }else{
            cin>>k;
            int z=lca(x,y);
            ll res=0,ans=0;
            msg cc=gets(x)+gets(y)-gets(z)-gets(fa[z]);
            res=al-cc.pf.gets();
        //    cout<<cc.sm<<" "<<cc.rs<<" "<<x<<" "<<y<<" "<<z<<endl;
            if(cc.rs<=k){
                print(res);
                puts("");
                continue;
            }
            int t=tr::solve(1,dfn[x],dfn[y],dfn[z],dfn[fa[z]],k,0,0);
            cc=gets(x,0,t)+gets(y,0,t)-gets(z,0,t)-gets(fa[z],0,t);
            res+=cc.pf.gets();
            cc=gets(x,t+1,1e9)+gets(y,t+1,1e9)-gets(z,t+1,1e9)-gets(fa[z],t+1,1e9);
            ans=cc.rs-t*cc.sm;res+=(ll)t*t*cc.sm;
            res-=(k-ans)*(2*t-1);
            print(res);
            puts("");
        }
    }
}