考虑到路径是有向的，不是很好维护。
如果路径无向的话，可以直接转化为链加和查询操作。
既然有向的话，不妨考虑一波hash。
对于一组询问x,y，可以把树划分为两颗子树。
合法显然需要满足
x子树的起点的hash=y子树的终点的hash
x子树的终点的hash=y子树的起点的hash
直接用LCT维护一个异或hash即可。

#include<iostream>
#include<cctype>
#include<cstdio>
#include<cstring>
#include<string>
#include<cmath>
#include<ctime>
#include<cstdlib>
#include<algorithm>
#define N 330000
#define L 300000
#define eps 1e-7
#define inf 1e9+7
#define db double
#define ll long long
#define ldb long double
using namespace std;
inline int read()
{char ch=0;int x=0,flag=1;while(!isdigit(ch)){ch=getchar();if(ch=='-')flag=-1;}while(isdigit(ch)){x=(x<<3)+(x<<1)+ch-'0';ch=getchar();}return x*flag;
}
#define lson son[x][0]
#define rson son[x][1]
struct lnk{int x,y,z;}p[N];
int va[N],vb[N],sa[N],sb[N],sa_[N],sb_[N],f[N],st[N],flag[N],son[N][2];
bool get(int x){return son[f[x]][1]==x;}
bool isroot(int x){return (son[f[x]][0]!=x)&&(son[f[x]][1]!=x);}
void pushup(int x)
{sa[x]=sa[lson]^sa[rson]^sa_[x]^va[x];sb[x]=sb[lson]^sb[rson]^sb_[x]^vb[x];
}
void update(int x){flag[x]^=1;swap(lson,rson);}
void pushdown(int x){if(!flag[x])return;if(lson)update(lson);if(rson)update(rson);flag[x]=0;}
void rotate(int x)
{int y=f[x],z=f[y],tx=get(x),ty=get(y),p=son[x][!tx];if(!isroot(y))son[z][ty]=x;son[x][!tx]=y;son[y][tx]=p;if(p)f[p]=y;f[y]=x;f[x]=z;pushup(y);pushup(x);
}
void splay(int x)
{int cnt=0,tmp=x;st[++cnt]=x;while(!isroot(x))st[++cnt]=f[x],x=f[x];for(int i=cnt;i>=1;i--)pushdown(st[i]);x=tmp;while(!isroot(x)){int y=f[x];if(!isroot(y))rotate(get(x)==get(y)?y:x);rotate(x);}pushup(x);
}
void access(int x)
{for(int y=0;x;y=x,x=f[x]){splay(x);sa_[x]^=sa[rson];sb_[x]^=sb[rson];rson=y;sa_[x]^=sa[rson];sb_[x]^=sb[rson];pushup(x);}
}
void makeroot(int x){access(x);splay(x);update(x);}
void link(int x,int y)
{makeroot(x);access(y);splay(y);f[x]=y;sa_[y]^=sa[x];sb_[y]^=sb[x];pushup(y);
}
void cut(int x,int y)
{makeroot(x);access(y);splay(y);f[x]=son[y][0]=0;pushup(y);
}
void add1(int x,int k){makeroot(x);va[x]^=k;pushup(x);}
void add2(int x,int k){makeroot(x);vb[x]^=k;pushup(x);}
int rng(){int x=0;for(int i=0;i<=30;i++)x^=(rand()%2)<<i;return x;}
int main()
{srand(time(0));read();int n=read(),m=read(),cnt=0,s=0;for(int i=1;i<n;i++){int x=read(),y=read();link(x,y);}for(int i=1;i<=m;i++){int flag=read();if(flag==1){int x,y;x=read();y=read();cut(x,y);x=read();y=read();link(x,y);}if(flag==2){cnt++;p[cnt].x=read();p[cnt].y=read();p[cnt].z=rng();add1(p[cnt].x,p[cnt].z);add2(p[cnt].y,p[cnt].z);s^=p[cnt].z;}if(flag==3){int k=read();add1(p[k].x,p[k].z);add2(p[k].y,p[k].z);s^=p[k].z;}if(flag==4){int x=read(),y=read();makeroot(x);access(y);int a=sa_[y]^va[y],b=sb_[y]^vb[y]; if((a^b)==s)printf("YES\n");else printf("NO\n");}}return 0;
}