#include<bits/stdc++.h>
using namespace std;
namespace my_std{
	#define ll long long
	#define bl bool
	ll my_pow(ll a,ll b,ll mod){
		ll res=1;
		if(!b) return 1;
		while(b){
			if(b&1) res=(res*a)%mod;
			a=(a*a)%mod;
			b>>=1;
		}
		return res;
	}
	ll qpow(ll a,ll b){
		ll res=1;
		if(!b) return 1;
		while(b){
			if(b&1) res*=a;
			a*=a;
			b>>=1;
		}
		return res;
	}
	#define db double
	#define pf printf
	#define pc putchar
	#define fr(i,x,y) for(register ll i=(x);i<=(y);i++)
	#define pfr(i,x,y) for(register ll i=(x);i>=(y);i--)
	#define go(u) for(ll i=head[u];i;i=e[i].nxt)
	#define enter pc('\n')
	#define space pc(' ')
	#define fir first
	#define sec second
	#define MP make_pair
	#define il inline
	#define inf 8e18
	#define random(x) rand()*rand()%(x)
	#define inv(a,mod) my_pow((a),(mod-2),(mod))
	il ll read(){
		ll sum=0,f=1;
		char ch=0;
		while(!isdigit(ch)){
			if(ch=='-') f=-1;
			ch=getchar();
		}
		while(isdigit(ch)){
			sum=sum*10+(ch^48);
			ch=getchar();
		}
		return sum*f;
	}
	il void write(ll x){
		if(x<0){
			x=-x;
			pc('-');
		}
		if(x>9) write(x/10);
		pc(x%10+'0');
	}
	il void writeln(ll x){
		write(x);
		enter;
	}
	il void writesp(ll x){
		write(x);
		space;
	}
}
using namespace my_std;
ll n,q,tree[100010],ans[100010];
struct edge{
	ll nxt,to;
};
struct node{
	ll x,y;
}a[100010];
struct Node{
	ll fr,sc,t,id;
}b[200020],c[300030];
il bl operator<(const Node &x,const Node &y){
	if(x.fr!=y.fr) return x.fr<y.fr;
	if(x.sc!=y.sc) return x.sc<y.sc;
	return x.id<y.id;
}
struct tree{
	ll head[100010],cnt=0,pos[100010],id[100010],len[100010],tot=0,sta[100010],top=0;
	ll st[100010],ed[100010],tott=0,dep[100010],a[100010];
	bl vis[100010],ck[100010];
	edge e[200020];
	void add(ll u,ll v){
		e[++cnt].nxt=head[u];
		e[cnt].to=v;
		head[u]=cnt;
	}
	void dfs0(ll u){
		vis[u]=1;
		id[u]=tot;
		go(u){
			ll v=e[i].to;
			if(!vis[v]) dfs0(v);
		}
	}
	void dfs1(ll u){
		vis[u]=1;
		sta[++top]=u;
		ll v=a[u];
		if(!vis[v]) dfs1(v);
		else if(!ck[u]){
			ll tmp=top;
			while(1){
				ck[sta[tmp]]=1;
				pos[sta[tmp]]=++len[id[u]];
				if(sta[tmp]==v) break;
				tmp--;
			}
		}
		vis[u]=0;
		top--;
	}
	void dfs2(ll fa,ll u){
		if(!ck[u]){
			st[u]=++tott;
			dep[u]=dep[fa]+1;
			pos[u]=(pos[fa]-1+len[id[u]])%len[id[u]];
		}
		go(u){
			ll v=e[i].to;
			if(ck[v]||v==fa) continue;
			dfs2(u,v);
		}
		if(!ck[u]) ed[u]=tott;
	}
	void init(){
		fr(i,1,n){
			a[i]=read();
			add(i,a[i]);
			add(a[i],i);
		}
		fr(i,1,n){
			if(!id[i]){
				tot++;
				dfs0(i);
			}
		}
		fr(i,1,n) vis[i]=0;
		fr(i,1,n) if(!len[id[i]]) dfs1(i);
		fr(i,1,n) if(ck[i]) pos[i]=len[id[i]]-pos[i];
		fr(i,1,n) if(ck[i]) dfs2(0,i);
		return;
	}
}F,G;
il ll lowbit(ll x){
	return x&(-x);
}
il void mdf(ll x,ll v){
	while(x<=n){
		tree[x]+=v;
		x+=lowbit(x);
	}
}
il ll query(ll x){
	ll res=0;
	while(x){
		res+=tree[x];
		x-=lowbit(x);
	}
	return res;
}
void solve1(){
	map<pair<pair<ll,ll>,ll>,bl> mp;
	fr(i,1,n){
		if(F.ck[i]&&G.ck[i]){
			ll len=__gcd(F.len[F.id[i]],G.len[G.id[i]]);
			mp[MP(MP(F.id[i],G.id[i]),((F.pos[i]-G.pos[i])%len+len)%len)]=1;
		}
	}
	fr(i,1,q){
		ll len=__gcd(F.len[F.id[a[i].x]],G.len[G.id[a[i].y]]);
		if(mp.count(MP(MP(F.id[a[i].x],G.id[a[i].y]),((F.pos[a[i].x]-G.pos[a[i].y])%len+len)%len))) ans[i]=1;
	}
}
void solve2(){
	ll cnt=0;
	fr(i,1,n) if(!F.ck[i]&&G.ck[i]) b[++cnt]=(Node){G.id[i],(G.pos[i]+F.dep[i])%G.len[G.id[i]],0,i};
	fr(i,1,q) if(!F.ck[a[i].x]) b[++cnt]=(Node){G.id[a[i].y],(G.pos[a[i].y]+F.dep[a[i].x])%G.len[G.id[a[i].y]],0,n+i};
	sort(b+1,b+cnt+1);
	ll lst=1,tot;
	fr(i,1,cnt){
		if(i==cnt||b[i].fr!=b[i+1].fr||b[i].sc!=b[i+1].sc){
			tot=0;
			fr(j,lst,i){
				if(b[j].id<=n) c[++tot]=(Node){F.dep[b[j].id],0,0,b[j].id};
				else c[++tot]=(Node){F.dep[a[b[j].id-n].x]-G.dep[a[b[j].id-n].y],0,0,b[j].id};
			}
			sort(c+1,c+tot+1);
			fr(j,1,tot){
				if(c[j].id<=n){
					mdf(F.st[c[j].id],1);
					mdf(F.ed[c[j].id]+1,-1);
				}
				else if(query(F.st[a[c[j].id-n].x])) ans[c[j].id-n]=1;
			}
			fr(j,1,tot){
				if(c[j].id<=n){
					mdf(F.st[c[j].id],-1);
					mdf(F.ed[c[j].id]+1,1);
				}
			}
			lst=i+1;
		}
	}
}
void solve3(){
	ll cnt=0;
	fr(i,1,n) if(!F.ck[i]&&!G.ck[i]) b[++cnt]=(Node){F.dep[i]-G.dep[i],0,0,i};
	fr(i,1,q) if(!F.ck[a[i].x]&&!G.ck[a[i].y]) b[++cnt]=(Node){F.dep[a[i].x]-G.dep[a[i].y],0,0,n+i};
	sort(b+1,b+cnt+1);
	ll lst=1,tot;
	fr(i,1,cnt){
		if(i==cnt||b[i].fr!=b[i+1].fr){
			tot=0;
			fr(j,i,lst){
				if(b[j].id<=n){
					c[++tot]=(Node){F.st[b[j].id],0,1,b[j].id};
					c[++tot]=(Node){F.ed[b[j].id]+1,0,-1,b[j].id};
				}
				else c[++tot]=(Node){F.st[a[b[j].id-n].x],0,0,b[j].id};
			}
			sort(c+1,c+tot+1);
			fr(j,1,tot){
				if(c[j].id<=n){
					mdf(G.st[c[j].id],c[j].t);
					mdf(G.ed[c[j].id]+1,-c[j].t);
				}
				else if(query(G.st[a[c[j].id-n].y])) ans[c[j].id-n]=1;
			}
			fr(j,1,tot){
				if(c[j].id<=n){
					mdf(G.st[c[j].id],-c[j].t);
					mdf(G.ed[c[j].id]+1,c[j].t);
				}
			}
			lst=i+1;
		}
	}
}
int main(){
	n=read();
	q=read();
	F.init();
	G.init();
	fr(i,1,q){
		a[i].x=read();
		a[i].y=read();
	}
	solve1();
	solve3();
	solve2();
	swap(F,G);
	solve2();
	fr(i,1,q){
		if(ans[i]) pf("YES\n");
		else pf("NO\n");
	}
}