#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=2e5+5,M=N*60+5,K=1e7+5,mod=998244353,Mod=mod-1;const db eps=1e-9;const ll INF=3e13+7;mt19937 rnd(263082);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;
int n,q,fa[N],A[N],B[N];
vector<int> S[N];
int d[N],tp[N],ed[N],siz[N],son[N],id[N],ih;
ll mx[N];
void dfs1(int x,int La){
	d[x]=d[La]+1;siz[x]=1;mx[x]=int(S[x].size()+1)*100000000ll;
	for(int i:S[x]) dfs1(i,x),siz[x]+=siz[i],siz[i]>siz[son[x]]&&(son[x]=i),mx[x]=max(mx[x],int(S[i].size()+1)*100000000ll);
}
void dfs2(int x,int La){
	tp[x]=La;id[x]=++ih;ed[tp[x]]=ih;if(son[x]) dfs2(son[x],La);
	for(int i:S[x]) if(i^son[x]) dfs2(i,i);
}
namespace DS1{
	int cnt,L[M],R[M];
	ll sum[M],mi[M];
	int rt[N],st[M],sh;
	void up(int v,ll l,ll r){
		ll m=l+r>>1;
		sum[v]=(L[v]?sum[L[v]]:-(m-l+1))+(R[v]?sum[R[v]]:-(r-m));
		mi[v]=min((L[v]?mi[L[v]]:-(m-l+1))+(R[v]?sum[R[v]]:-(r-m)),R[v]?mi[R[v]]:-(r-m));
	}
	void clr(int &v){
		L[v]=R[v]=sum[v]=mi[v]=0;
		st[++sh]=v;v=0;
	}
	void modify(ll x,ll y,int &v,ll l=0,ll r=INF){
		if(!v) v=(sh?st[sh--]:++cnt),sum[v]=mi[v]=-(r-l+1);
		if(l==r){
			sum[v]+=y;mi[v]+=y;
			return;
		}
		ll m=l+r>>1;x<=m?modify(x,y,L[v],l,m):modify(x,y,R[v],m+1,r);up(v,l,r);
		if(sum[v]==-(r-l+1)) clr(v);
	}
	void add(int p,ll x,ll y){
		modify(x,y,rt[p],0,mx[p]);
	}
	ll find(ll x,int v,ll l=0,ll r=INF){
		if(l==r) return l;
		if(!v) return r-x+1;
		ll m=l+r>>1;
		return x+(R[v]?mi[R[v]]:-(r-m))>0?find(x+(R[v]?sum[R[v]]:-(r-m)),L[v],l,m):find(x,R[v],m+1,r);
	}
	ll qry(int p,ll x){
		return find(mx[p]-x,rt[p],0,mx[p]);
	}
}
struct node{
	ll x,A,B;
	ll calc(ll y)const{return y<x?A:B;}
}ans;
node operator +(const node &A,const node &B){
	return (node){A.x,B.calc(A.A),B.calc(A.B)};
}
namespace DS2{
	#define ls v<<1
	#define rs v<<1|1
	node f[M];
	void up(int v){f[v]=f[rs]+f[ls];}
	void modify(int x,node y,int l=1,int r=n,int v=1){
		if(l==r){f[v]=y;return;}int m=l+r>>1;
		x<=m?modify(x,y,l,m,ls):modify(x,y,m+1,r,rs);up(v);
	}
	void qry(int x,int y,int l=1,int r=n,int v=1){
		if(x<=l&&r<=y){ans=ans+f[v];return;}int m=l+r>>1;
		y>m&&(qry(x,y,m+1,r,rs),0);x<=m&&(qry(x,y,l,m,ls),0);
	}
	#undef ls
	#undef rs
}
ll dp[N],sum[N];
ll qry(int x){
	ans=(node){INF,0,0};
	DS2::qry(id[x],ed[tp[x]]);
	return ans.A;
}
void remake(int x){
	ll w=DS1::qry(x,sum[x]);
	if(!son[x]){
		DS2::modify(id[x],(node){INF,w,0});
	}else{
		DS2::modify(id[x],(node){w,w,DS1::qry(x,sum[x]-B[son[x]])});
	}
}
void make(int x,int La){
	sum[x]=A[x];
	for(int i:S[x]){
		make(i,x);
		if(i^son[x]) DS1::add(x,dp[i],B[i]);
		sum[x]+=B[i];
	}
	remake(x);
	dp[x]=qry(x);
}
void modify(int p,int x,int y){
	sum[p]-=A[p];A[p]=x;sum[p]+=A[p];
	remake(p);
	if(p^1){
		sum[fa[p]]-=B[p];
		if(tp[p]==p){
			DS1::add(fa[p],dp[p],-B[p]);
		}
	}
	B[p]=y;
	dp[p]=qry(p);
	if(p^1){
		sum[fa[p]]+=B[p];
		if(tp[p]==p){
			DS1::add(fa[p],dp[p],B[p]);
		}
	}
	if(p==1) return;
	p=fa[p];remake(p);
	while(p){
		p=tp[p];
		if(p^1) DS1::add(fa[p],dp[p],-B[p]);
		dp[p]=qry(p);
		if(p^1) DS1::add(fa[p],dp[p],B[p]),remake(fa[p]);
		p=fa[p];
	}
}
void Solve(){
	scanf("%d%d",&n,&q);
	for(int i=2;i<=n;i++) scanf("%d",&fa[i]),S[fa[i]].push_back(i);
	dfs1(1,0);
	dfs2(1,1);
	for(int i=1;i<=n;i++) scanf("%d",&A[i]);
	for(int i=1;i<=n;i++) scanf("%d",&B[i]);
	make(1,0);
	while(q--){
		int op,p,x,y;
		scanf("%d",&op);
		if(op==1) scanf("%d%d%d",&p,&x,&y),modify(p,x,y);
		else{
			scanf("%d%d",&x,&y);
			printf("%d\n",make_pair(qry(x),x)<make_pair(qry(y),y));
		}
	}
}
int main(){
	int t=1;
	// scanf("%d",&t);
	while(t--) Solve();
	cerr<<clock()*1.0/CLOCKS_PER_SEC<<'\n';
}