分析：

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<assert.h>
#define SF scanf
#define PF printf
#define MAXN 200010
#define MOD 1000000009
using namespace std;
typedef long long ll;
struct node *NIL;
struct node{
    node *ch[2],*fa;
    int val,siz;
    bool Dir(){
        return this==fa->ch[1];
    }
    void setchild(node *x,int d){
        ch[d]=x;
        if(x!=NIL)
            x->fa=this;
    }
    void pushup(){
        siz=ch[0]->siz+ch[1]->siz+1;
    }
}tree[MAXN*2];
int fax[MAXN];
node *lc[MAXN],*rc[MAXN];
node * Newnode(node *x,int val){
    x->ch[0]=x->ch[1]=x->fa=NIL;
    x->val=val;
    x->siz=1;
    return x;
}
void Rotate(node *x){
    node *y=x->fa;
    int d=x->Dir();
    if(y->fa==NIL)
        x->fa=NIL;
    else
        y->fa->setchild(x,y->Dir());
    y->setchild(x->ch[!d],d);
    x->setchild(y,!d);
    y->pushup();
}
void Splay(node *x,node *rt){
    while(x->fa!=rt){
        node *y=x->fa;
        if(y->fa==rt){
            Rotate(x);
            break;
        }
        if(x->Dir()==y->Dir())
            Rotate(y);
        else
            Rotate(x);
        Rotate(x);
    }
    x->pushup();
}
node *find_nxt(node *x,int d){
	while(x->ch[d]!=NIL)
		x=x->ch[d];
	return x;	
}
int check(int a,int b){
	Splay(lc[a],NIL);
	node *rta=find_nxt(lc[a],0);
	Splay(rta,NIL);
	
	Splay(lc[b],NIL);
	node *rtb=find_nxt(lc[b],0);
	Splay(rtb,NIL);
	
	if(rta!=rtb)
		return 0;
	
	Splay(lc[a],NIL);
	int siz1=lc[a]->ch[0]->siz;
	Splay(rc[a],NIL);
	int siz2=rc[a]->ch[0]->siz;
	Splay(lc[b],NIL);
	int siz=lc[b]->ch[0]->siz;
	if(siz1<siz&&siz<siz2)
		return 1;
	if(fax[rta->val]!=0){
		node *x=lc[fax[rta->val]];
		Splay(x,NIL);
		int sizx=x->ch[0]->siz;
		if(siz1<=sizx&&sizx<=siz2)
			return 1;	
	}
	return 0;
}
void cut(int x){
	node *a=lc[x];
	node *b=rc[x];
	Splay(a,NIL);
	if(a->ch[0]==NIL){
		fax[x]=0;
		return ;
	}
	node *rt=find_nxt(a,0);
	Splay(rt,NIL);
	if(fax[rt->val]==0||check(x,fax[rt->val])==0){
		Splay(rt,NIL);
		Splay(a,rt);
		Splay(b,a);
		node *t=find_nxt(b->ch[1],0);
		Splay(t,b);
		rt->setchild(t,1);
		t->setchild(a->ch[0],0);
		a->fa=NIL;
		a->ch[0]=NIL;
		b->ch[1]=NIL;
		t->pushup();
		rt->pushup();
		b->pushup();
		a->pushup();//cut a from x
	}
	else{
		node *c=lc[fax[rt->val]];
		fax[rt->val]=0;
		assert(rt->ch[0]==NIL);
		Splay(rt,NIL);
		Splay(a,rt);
		Splay(b,a);
		node *t=find_nxt(b->ch[1],0);
		Splay(t,b);
		rt->setchild(t,1);
		t->setchild(a->ch[0],0);
		a->fa=NIL;
		a->ch[0]=NIL;
		b->ch[1]=NIL;
		t->pushup();
		rt->pushup();
		b->pushup();
		a->pushup();//cut a from x
		
		//PF("{%d %d}\n",a->ch[0]-tree,a->ch[1]-tree);
		
		Splay(c,NIL);
		node *d=find_nxt(c->ch[1],0);
		Splay(d,c);
		d->setchild(rt,0);
		d->pushup();
		c->pushup();
	}
}
void link(int a,int b){
	Splay(lc[a],NIL);
	assert(lc[a]->ch[0]==NIL);
	if(check(a,b)||a==b){//we can reach a from b
		fax[a]=b;
	}
	else{
		Splay(lc[a],NIL);
		node *c=lc[b];
		Splay(c,NIL);
		node *d=find_nxt(c->ch[1],0);
		Splay(d,c);
		d->setchild(lc[a],0);
		d->pushup();
		c->pushup();
	}
}
int n,m;
int main(){
	freopen("repeater.in","r",stdin);
	freopen("repeater.out","w",stdout);
	int tag,a,b;
    NIL=&tree[0];
    NIL->ch[0]=NIL->ch[1]=NIL->fa=NIL;
    SF("%d%d",&n,&m);
	for(int i=1;i<=n;i++){
    	lc[i]=Newnode(&tree[i],i);
    	rc[i]=Newnode(&tree[i+n],i);
		lc[i]->setchild(rc[i],1);
	}
	ll ans=0;
	int cnt=0;
	for(int i=1;i<=m;i++){
		//PF("[now,begin %d]:\n",i);
		SF("%d%d%d",&tag,&a,&b);	
		if(tag==1){
			cut(a);
			if(b!=0)
				link(a,b);
		}
		else{
			//PF("{%d}\n",check(b,a));
			ans=(ans*2ll+check(b,a))%MOD;
		}
		/*for(int i=1;i<=n;i++){
			PF("fa:(%d)",fax[i]);
			PF("<%d,(%d),%d> | <%d,(%d),%d>\n",lc[i]->ch[0]-tree,lc[i]-tree,lc[i]->ch[1]-tree,rc[i]->ch[0]-tree,rc[i]-tree,rc[i]->ch[1]-tree);	
		}*/
	}
	PF("%lld",ans);
}