#include<bits/stdc++.h>
using namespace std;
using ll=long long;
using pi=pair<int,int>;
using pl=pair<ll,ll>;
#define fi first
#define se second
const int N=2e5+5;
int type,n,m,sn,fa[N],rt[N],a[N],b[N],sz[N],son[N],L[N],ed[N],top[N],ps[N],g[N];
ll f[N][2],lf[N];
vector<int>e[N];
mt19937 rd(5384);
struct Mat{
	bool v[2];
	Mat(int p=0){v[0]=0,v[1]=p;}
    Mat(int x,int y){v[0]=x,v[1]=y;}
	Mat operator*(const Mat&t){return Mat(t.v[v[0]],t.v[v[1]]);}
}to[N];
struct sgt{
	Mat t[N<<2];
	void upd(int p){t[p]=t[p<<1|1]*t[p<<1];}
	void build(int p,int l,int r) {
		if(l==r)return t[p]=to[ps[l]],void();int mid=l+r>>1;
		build(p<<1,l,mid),build(p<<1|1,mid+1,r),upd(p);
	}
	void mdf(int p,int x,int l=1,int r=n) {
		if(l==r)return t[p]=to[ps[x]],void();int mid=l+r>>1;
		if(x<=mid)mdf(p<<1,x,l,mid);else mdf(p<<1|1,x,mid+1,r);upd(p);
	}
	Mat ask(int p,int ql,int qr,int l=1,int r=n) {
		if(ql>qr)return Mat(1);
		if(ql<=l&&qr>=r)return t[p];int mid=l+r>>1;Mat s(1);
		if(ql<=mid)s=ask(p<<1,ql,qr,l,mid);if(qr>mid)s=ask(p<<1|1,ql,qr,mid+1,r)*s;
		return s;
	}
}sg;
struct fhq{
    int sz,st[N*2],ch[N*2][2],R[N*2];ll s[N*2],mx[N*2];pl v[N*2];
    void upd(int p) {
        s[p]=v[p].se+s[ch[p][0]]+s[ch[p][1]];ll S=s[ch[p][0]]+v[p].se;
        mx[p]=min(v[p].fi-S,min(mx[ch[p][0]],mx[ch[p][1]]-S));
    }
    int New(){return st[0]?st[st[0]--]:++sz;}
    void jq(int x){st[++st[0]]=x,ch[x][0]=ch[x][1]=0;}
    pi split(int p,pl k) {
        if(!p)return {0,0};pi w;
        if(k>=v[p])return w=split(ch[p][1],k),ch[p][1]=w.fi,upd(p),(pi){p,w.se};
        return w=split(ch[p][0],k),ch[p][0]=w.se,upd(p),(pi){w.fi,p};
    }
    int merge(int p,int q) {
        if(!p||!q)return p+q;
        if(R[p]<R[q])return ch[p][1]=merge(ch[p][1],q),upd(p),p;
        return ch[q][0]=merge(p,ch[q][0]),upd(q),q;
    }
    void ins(int&p,pl x) {
        pi w=split(p,x);int q=New();
        R[q]=rd(),v[q]=x,s[q]=x.se,mx[q]=x.fi-x.se;
        p=merge(w.fi,merge(q,w.se));
    }
    void del(int&p,pl x) {
        pi w1=split(p,x),w2=split(w1.fi,{x.fi,x.se-1});
        int q=merge(ch[w2.se][0],ch[w2.se][1]);
        p=merge(w2.fi,merge(q,w1.se)),jq(w2.se);
    }
    ll qry(int p,ll k) {
    	if(!p)return 0;ll nk=k+v[p].se+s[ch[p][0]];
        if(mx[ch[p][1]]<nk)return qry(ch[p][1],nk)+v[p].se+s[ch[p][0]];
        if(v[p].fi<nk)return v[p].se+s[ch[p][0]];
		return qry(ch[p][0],k);
    }
}T;
ll calc(int x,ll v){return v+T.qry(rt[x],v);}
ll get(int x){return sg.ask(1,L[x]+1,ed[x]).v[1];}
ll F(int x,int y=-1){return calc(x,a[x]+(y==-1?get(x):y)*b[son[x]]);}
void dfs1(int x,int p) {
    sz[x]=1;
    for(int y:e[x]) {
        dfs1(y,x),sz[x]+=sz[y];
        if(sz[y]>sz[son[x]])son[x]=y;
    }
}
void dfs2(int x,int tp) {
    top[x]=tp,L[x]=++sn,ps[sn]=x;
    if(son[x])dfs2(son[x],tp),ed[x]=ed[son[x]];
	else return ed[x]=sn,f[x][0]=f[x][1]=a[x],g[x]=1,void();
    for(int y:e[x])if(y!=fa[x]&&y!=son[x])dfs2(y,y),T.ins(rt[x],{f[y][g[y]],b[y]});
    for(int i=0;i<2;i++)f[x][i]=calc(x,a[x]+b[son[x]]*i);
    for(int i=0;i<2;i++)if(f[x][1]>f[son[x]][i])to[son[x]].v[i]=1;else to[son[x]].v[i]=0;
    g[x]=to[son[x]].v[g[son[x]]];
}
void Mdf(int x,int y,int z) {
	for(int i=x;i;i=fa[i])i=top[i],lf[i]=F(i);
	int sx=x,lb=b[x];a[x]=y,b[x]=z;
	while(x) {
		ll f0=F(x,0),f1=F(x,1);
		if(son[x])to[son[x]].v[0]=(f1>F(son[x],0)),to[son[x]].v[1]=(f1>F(son[x],1)),sg.mdf(1,L[x]+1);
        if(x!=top[x]) {
            int p=fa[x];ll fp0=F(p,1),fp1;
            to[x].v[0]=(fp0>f0),to[x].v[1]=(fp0>f1),sg.mdf(1,L[x]);
            if(p!=top[x]&&x==sx)fp1=F(fa[p],1),to[p].v[0]=(fp1>F(p,0)),to[p].v[1]=(fp1>fp0),sg.mdf(1,L[x]-1);
        }x=top[x];
        if(fa[x])T.del(rt[fa[x]],{lf[x],(x==sx?lb:b[x])}),T.ins(rt[fa[x]],{F(x),b[x]});
        x=fa[x];
	}
}
int main() {
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    cin>>n>>m,T.mx[0]=4e18;
    for(int i=2;i<=n;i++)cin>>fa[i],e[fa[i]].push_back(i);
    for(int i=1;i<=n;i++)cin>>a[i];
    for(int i=1;i<=n;i++)cin>>b[i];
    dfs1(1,0),dfs2(1,1),sg.build(1,1,n);
    while(m--) {
    	int op,x,y,z;cin>>op>>x>>y;
    	if(op==1)cin>>z,Mdf(x,y,z);
    	else {
    		ll vx=F(x),vy=F(y);
    		cout<<(vx==vy?x<y:vx<vy)<<'\n'; 
		}
	}
    return 0;
}