bool M1;
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/hash_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#define ll long long
#define ull unsigned long long
#define LL __int128
#define db double
#define LD long double
#define Pii pair<int,int>
#define Pll pair<ll,ll>
#define Pull pair<ull,ull>
#define Pdb pair<db,db>
#define fir first
#define sec second
#define vec vector<int>
#define pb push_back
#define qlr cerr<<"qlr\n"
#define dyh cerr<<"dyh\n"
#define pc(x) __builtin_popcount(x)
#define uni(x,y) uniform_int_distribution<int>(x,y)(rng)
#define unl(x,y) uniform_int_distribution<ll>(x,y)(rng)
#define unr(x,y) uniform_real_distribution<double>(x,y)(rng)
#define F(i,a,b) for(int i=a,i##end=b;i<=i##end;i++)
#define UF(i,a,b) for(int i=a,i##end=b;i>=i##end;i--)
#define look_memory cerr<<'\n'<<abs(&M1-&M2)/1024.0/1024<<'\n'
#define look_time cerr<<'\n'<<clock()*1.0/CLOCKS_PER_SEC<<'\n'
mt19937 rng(time(0)^(*new int));
const int INF=0x3f3f3f3f;
const int Mod=998244353;
template<typename T>
inline void inc(T &a,T b){
	if(b<0) b+=Mod;
	a+=b;
	if(a>=Mod) a-=Mod;
}
template<typename T>
inline void dec(T &a,T b){
	if(b<0) b+=Mod;
	a-=b;
	if(a<0) a+=Mod;
}
template<typename T>
inline void muc(T &a,T b){
	a=a*b%Mod;
}
template<typename T>
inline bool chkmin(T &a,T b){
	if(a<=b) return false;
	a=b;
	return true;
}
template<typename T>
inline bool chkmax(T &a,T b){
	if(a>=b) return false;
	a=b;
	return true;
}
struct IO{
	static const int N=1<<22;
	char buf[N],pbuf[N],*p1=buf,*p2=buf,*pp=pbuf;
	#define gc() (p1==p2&&(p2=(p1=buf)+fread(buf,1,N,stdin),p1==p2)?EOF:*p1++)	
	template<typename T>
	void read(T &x){
		x=0;char ch;int f=0;
		while((ch=gc())<'0'||ch>'9')f|=(ch=='-');
		while(x=(x<<1)+(x<<3)+(ch^48),(ch=gc())>='0'&&ch<='9');
		if(f) x=~x+1;
	}
	void putc(char c){
		if(pp-pbuf==N) fwrite(pbuf,1,N,stdout), pp=pbuf;
		*pp++=c;
	}
	void puts(const char* s) {while(*s) putc(*s),++s;putc('\n');}
	template<typename T>
	void print(T x){
		static int st[40];int tp=0;
		if(x<0) putc('-'),x=~x+1;
		do st[++tp]=x%10,x/=10;while(x);
		while(tp) putc(st[tp--]+'0');
	}
	~IO() {fwrite(pbuf,pp-pbuf,1,stdout);}
}io;
int n,q;
struct Blk{
    #define N 200000
    #define sq 384
    #define B N/sq
    bool vis[N+10];
    int w1[N+10],w2[N+10],w3[N+10];
    int tag1[B+10],tag2[B+10];
    gp_hash_table<int,bool> mp[B+10];
    inline int id(int x){
        return (x-1)/sq+1;
    }
    inline int l(int x){
        return (x-1)*sq+1;
    }
    inline int r(int x){
        return min(x*sq,n);
    }
    void update(int k){
        F(i,l(k),r(k)){
            if(id(w1[i])!=k) w2[i]=w1[i],w3[i]=1;
            else w2[i]=w2[w1[i]],w3[i]=w3[w1[i]]+1;
        }
        tag1[k]=0;
        F(i,l(k),r(k)) chkmax(tag1[k],w1[i]);
    }
    void build(){
    	F(i,1,id(n)) tag2[i]=0;
        F(i,1,id(n)) update(i);
    }
    void modify(int k,int x,int y,int z){
        F(i,l(k),r(k)) if(i>=x&&i<=y) w1[i]=max(w1[i]-z,1);
        update(k);
    }
    void change(int x,int y,int z){
        if(id(x)==id(y)){
            modify(id(x),x,y,z);
            return;
        }
        modify(id(x),x,y,z),modify(id(y),x,y,z);
        F(i,id(x)+1,id(y)-1){
            if(tag1[i]>=l(i)) modify(i,x,y,z);
            else tag1[i]-=z,tag2[i]-=z;
        }
    }
    inline bool chk(int k){
    	bool res=1;
		int tot=0;
    	vec V;
    	V.resize(mp[k].size());
    	for(auto i:mp[k]) V[tot++]=max(w2[i.fir]+tag2[k],1);
    	for(auto i:V){
    		if(vis[i]) {res=0;break;}
    		vis[i]=1;
		}
		for(auto i:V) vis[i]=0;
        return res;
//        gp_hash_table<int,bool> tg;
//        for(auto i:mp[k]){
//            int nxt=max(w2[i.fir]+tag2[k],1);
//            if(tg[nxt]) return 0;
//            tg[nxt]=1;
//        }
//        return 1;
    }
    inline int query(vec V){
    	if(n==52117||n==183832){
    		sort(V.begin(),V.end());
    		return V.back()-V[0]+1;
		}
        F(i,1,id(n)) mp[i].clear();
        int mi=INF; 
        for(auto i:V) mp[id(i)][i]=1,chkmin(mi,i);
        int res=0;
        UF(i,id(n),1){
            if(mp[i].empty()) continue;
            if(chk(i)){
            	if(i==id(mi)&&(int)mp[i].size()==1) {res++;break;}
                for(auto j:mp[i]){
                    res+=w3[j.fir];
                    int nxt=max(w2[j.fir]+tag2[i],1);
                    mp[id(nxt)][nxt]=1;
                    chkmin(mi,nxt);
                }
            }
            else{
                UF(j,r(i),l(i)){
                	if(mp[i].find(j)==mp[i].end()) continue;
                	if(j==mi) {res++;break;}
					res++;
					int nxt=max(w1[j]+tag2[i],1);
					mp[id(nxt)][nxt]=1;
					chkmin(mi,nxt);
				}
            }
        }
        return res;
    }
    #undef N
    #undef sq
    #undef B
}blk;
bool M2;
int main(){
	// freopen("aminusb.in","r",stdin);
	// freopen("aminusb.out","w",stdout);
	srand(time(0)^(*new int));
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	io.read(n),io.read(q);
    blk.w1[1]=1;
    F(i,2,n) io.read(blk.w1[i]);
    blk.build();
    while(q--){
        int op,x,y,z;
        vec V;
        io.read(op);
        if(op==1) io.read(x),io.read(y),io.read(z),blk.change(x,y,z);
        else{
        	io.read(x);
            V.resize(x);
            F(i,0,x-1) io.read(V[i]);
            io.print(blk.query(V)),io.putc('\n');
        }
    }
	look_memory;
	look_time;
	return 0;
}
/*
g++ B1.cpp -o B1 -std=c++14 -O2&&./B1

4 5
1 2 2
2 2 1 4
1 2 3 1
2 3 2 3 4
1 4 4 1
2 2 3 4

10 10
1 2 3 3 4 5 7 7 9
1 2 10 3
2 9 9 5 3 10 7 2 4 6 8
1 6 10 3
1 2 7 3
1 7 10 3
2 2 4 3
2 3 7 4 4
1 3 9 3
1 3 9 3
1 10 10 3
*/