#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef double dou;
typedef pair<int,int> pii;
#define fi first
#define se second
#define mapa make_pair
typedef long double ld;
typedef unsigned long long ull;
#define ep emplace_back
template <typename T>inline void read(T &x){
	x=0;char c=getchar();bool f=0;
	for(;c<'0'||c>'9';c=getchar()) f|=(c=='-');
	for(;c>='0'&&c<='9';c=getchar())
	x=(x<<1)+(x<<3)+(c^48);
	x=(f?-x:x);
}
const int N=2e5+5;
const int B=500;
int n, m;
int lp[N], rp[N], bid[N];
int fa[N], nxt[N], dis[N];
int dt[N];
inline void rebuild(int i){
	if(dt[i]>=B) return ;
	for(int j=lp[i]; j<=rp[i]; ++j){
		int x=j; dis[j]=0;
		while(x>=lp[i]) ++dis[j], x=max(1, fa[x]-dt[i]);
		nxt[j]=x;
	}
}
#define gf(x) (dt[bid[x]]<B?nxt[x]:max(1, fa[x]-dt[bid[x]]))
inline int lca(int x, int y){
	while(gf(x)^gf(y)){
		if(x<y) y=gf(y);
		else x=gf(x);
	}
	if(bid[x]!=bid[y]) return gf(x);
	while(x^y){
		if(x<y) y=max(1, fa[y]-dt[bid[y]]);
		else x=max(1, fa[x]-dt[bid[x]]);
	}
	return x;
}
inline int dep(int x){
	int ret=0;
	while(x^1){
		if(dt[bid[x]]<B) ret+=dis[x], x=nxt[x];
		else ++ret, x=max(1, fa[x]-dt[bid[x]]);
	}
	return ret;
}
inline int getd(int x, int y){
	if(x==y) return 0;
	return dep(x)+dep(y)-2*dep(lca(x, y));
}
inline int jump(int x, int t){
	while(gf(x)>t) x=gf(x);
	while(fa[x]-dt[bid[x]]>t) x=fa[x]-dt[bid[x]];
	return x;
}
inline bool cmp(int x, int y){
	if(x==y)  return false;
	int t=lca(x, y);
	if(t==x) return true;
	if(t==y) return false;
	return jump(x, t)<jump(y, t);
}
int main(){
	read(n); read(m);
	for(int i=2; i<=n; ++i) read(fa[i]);
	for(int i=2; i<=n; ++i) bid[i]=(i-2)/B+1;
	bid[1]=0; 
	lp[0]=rp[0]=1; dt[0]=B;
	for(int i=1; i<=bid[n]; ++i) lp[i]=rp[i-1]+1, rp[i]=rp[i-1]+B;
	rp[bid[n]]=n;
	for(int i=1; i<=bid[n]; ++i) rebuild(i);
	while(m--){
		int op; read(op);
		if(op==1){
			int l, r, d; read(l); read(r); read(d);
			if(bid[l]==bid[r]){
				for(int i=l; i<=r; ++i) fa[i]-=d;
				rebuild(bid[l]);
				continue;
			}
			for(int i=l; i<=rp[bid[l]]; ++i) fa[i]-=d;
			rebuild(bid[l]);
			for(int i=lp[bid[r]]; i<=r; ++i) fa[i]-=d;
			rebuild(bid[r]);
			for(int i=bid[l]+1; i<bid[r]; ++i){
				dt[i]+=d;
				if(dt[i]<B) rebuild(i);
			}
		}
		else{
			int k, x; vector<int> vec;
			read(k);
			while(k--){
				read(x); vec.ep(x);
			}
			sort(vec.begin(), vec.end(), cmp);
			vec.ep(*vec.begin());
			int ans=0;
			for(int i=1; i<(int)vec.size(); ++i) ans+=getd(vec[i-1], vec[i]);
			ans>>=1;
			printf("%d\n", ans+1);
		}
	}
	return 0;
}