#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define pb push_back
#define ff first
#define ss second
#define INF 1000000001LL
#define POT (1LL<<20)
#define INFL 1000000000000000099LL
#define pii pair<ll,ll>
#define ppi pair<pii,ll>
#define pip pair<ll,pii>
#define ppp pair<pii,pii>
#define vi vector<ll>
#define vii vector<pii>
#define vvi vector<vi>
#define al(x) x.begin(),x.end()
#define rev(x) reverse(al(x))
#define FCTCST 7
template<typename T, typename U>
pair<T, U> operator+(const pair<T, U>& a, const pair<T, U>& b) {
return {a.first + b.first, a.second + b.second};
}
template<typename T, typename U>
pair<T, U> operator-(const pair<T, U>& a, const pair<T, U>& b) {
return {a.first - b.first, a.second - b.second};
}
template<typename T, typename U,typename Z>
pair<T, U> operator*(const pair<T, U>& a, const Z& b) {
return {a.first*b, a.second*b};
}
template<typename T, typename U,typename Z>
pair<T, U> operator/(const pair<T, U>& a, const Z& b) {
return {a.first/b, a.second/b};
}
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os<<"{"<<p.ff<<", "<<p.ss<<"}";
return os;
}
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
os << "{";
for (size_t i = 0; i < v.size(); ++i) {
if (i) os << ", ";
os << v[i];
}
os << "}";
return os;
}
template<ll MOD=998244353>
struct mint_t{
ll x;
mint_t(ll y=0){x=y%MOD;if(x<0)x+=MOD;}
mint_t& operator+=(const mint_t& a){if((x+=a.x)>=MOD)x-=MOD;return *this;}
mint_t& operator-=(const mint_t& a){if((x+=MOD-a.x)>=MOD)x-=MOD;return *this;}
mint_t operator+(const mint_t& a)const{mint_t res(*this);return res+=a;}
mint_t operator-(const mint_t& a)const{mint_t res(*this);return res-=a;}
mint_t& operator*=(const mint_t& a){(x*=a.x)%=MOD;return *this;}
mint_t operator*(const mint_t& a)const{mint_t res(*this);return res*=a;}
mint_t fp(ll y)const{
mint_t a=1,b=x;
while(y){
if(y&1)a*=b;
b*=b;
y/=2;
}
return a;
}
mint_t& operator/=(const mint_t& a){(*this)*=a.fp(MOD-2);return *this;}
mint_t operator/(const mint_t& a)const{mint_t res(*this);return res/=a;}
};
#define mint mint_t<>
template<long long MOD>
istream& operator>>(istream& in, mint_t<MOD>& a){
ll x;
in>>x;
a=mint_t<MOD>(x);
return in;
}
template<long long MOD>
istream& operator<<(istream& out, mint_t<MOD>& a){
out<<a.x;
return out;
}
mint fct[FCTCST];
mint bnm(ll a,ll b){
if(b>a || a<0)return 0;
return fct[a]/fct[b]/fct[a-b];
}
ll pop[10007],pop2[300];
vi g[10007];
ll mj[16];
ll zl[20007];
bool vs2[10007];
string ms[300];
string to_bin(ll x,ll bt){
string rs;
while(bt--){rs.pb('0'+x%2);x/=2;}
rev(rs);return rs;
}
ll to_int(string s){
ll rs=0;
for(char c:s){
rs*=2;rs+=c-'0';
}
return rs;
}
std::string aoi(int n, int m, int q, int k, std::vector<int> a,
std::vector<int> b, std::vector<long long> c,
std::vector<int> t, std::vector<int> x){
for(ll i=0;i<k;i++)zl[x[i]]=i+1;
for(ll i=0;i<m;i++){
g[a[i]].pb(i);g[b[i]].pb(i);
}assert(0);
for(ll i=0;i<n;i++)pop[i]=-2;while(n)n++;
priority_queue<pip,vector<pip>,greater<pip>>pq;
pq.push({0,{0,-1}});while(n)n++;
while(pq.size()){
pip x=pq.top();
pq.pop();
if(pop[x.ss.ff]!=-2)continue;
pop[x.ss.ff]=x.ss.ss;
for(ll i :g[x.ss.ff]){
pq.push({x.ff+c[i],{a[i]^b[i]^x.ss.ff,i}});
}
}
//for(ll i=0;i<n;i++)cout<<pop[i]<<" ";cout<<flush;
//cout<<"\n";
vvi v;while(n)n++;
for(ll i=0;i<q;i++){
mj[i]=300;
ll x=t[i];
vi pm;
while(pop[x]!=-1){
if(zl[pop[x]]){pm.pb(zl[pop[x]]-1);
if(vs2[pop[x]]){pm.pop_back();
mj[i]=pop[x];break;
}
vs2[pop[x]]=1;
}
x^=a[pop[x]]^b[pop[x]];
}
v.pb(pm);
}
v.pb({});
for(ll i=0;i<k;i++)if(!vs2[i])v.back().pb(i);
//for(ll i=0;i<q;i++)cout<<mj[i]<<" ";
//cout<<v<<flush;
while(n)n++;
vii v2;
for(ll i=0;i<v.size();i++){
v2.pb({v[i].size(),i});
}
sort(al(v2));
ll mr1=v2[0].ss,mr2=v2[1].ss;
if(mr1>mr2)swap(mr1,mr2);
//cout<<mr1<<" "<<mr2<<"\n";
string rs="";
for(vi i:v)rs.pb('0');
rs[mr1]=rs[mr2]='1';
for(ll i=0;i<v.size();i++){
ll x=i;
if(x==mr2)x=mr1;
if(x>mr2)x--;
string pm=to_bin(x,4);
if(x==mr1){
pm.pb('0'+(i!=x));
}
for(ll j:v[i])ms[j]=pm;
}
for(ll i=0;i<k;i++)rs+=ms[i]+to_bin(mj[i],9);
//cout<<rs<<endl;
return rs;
}
void answer(const std::vector<int> &e);
string gt(string& st,ll x){
string rs;
//if(st.size()<x)cout<<"xd"<<flush;
for(ll i=0;i<x;i++)rs.pb(st[i]);
for(ll i=0;i<x;i++)st.erase(st.begin());
return rs;
}
void bitaro(int n, int m, int q, int k, std::vector<int> a, std::vector<int> b,
std::vector<long long> c, std::vector<int> t, std::vector<int> x,
std::string s){
for(ll i=0;i<k;i++)zl[x[i]]=i+1;
vvi v(q+1);
ll mr1=-1,mr2;
for(ll i=0;i<=q;i++){
ll x=to_int(gt(s,1));
if(x)if(mr1==-1)mr1=i;else mr2=i;
}
//cout<<mr1<<" "<<mr2<<"\n"<<flush;
for(ll i=0;i<k;i++){
ll x=to_int(gt(s,4));//cout<<x<<" "<<flush;
if(x>=mr2)x++;
if(x==mr1)if(to_int(gt(s,1)))x=mr2;
v[x].pb(i);
mj[i]=to_int(gt(s,9));
//cout<<"xd"<<flush;
}
//for(ll i=0;i<k;i++)cout<<mj[i]<<" ";cout<<"\n";
//cout<<v<<"\n";
for(ll i=0;i<k;i++)pop2[i]=300;
for(ll i=0;i<q;i++){
for(ll i=0;i<n;i++)pop[i]=-2;
for(ll j=0;j<n;j++)g[j].clear();
while(mj[i]!=300){
//cout<<mj[i]<<" "<<pop[mj[i]]<<" "<<x[mj[i]];return;
v[i].pb(x[mj[i]]);
mj[i]=pop2[mj[i]];
}
for(ll j:x)c[j]=1000000000000001LL;
for(ll j:v[i]){
g[a[x[j]]].pb(x[j]);
g[b[x[j]]].pb(x[j]);
c[x[j]]=0;
//cout<<x[j]<<" ";
}
for(ll j=0;j<m;j++){
if(!zl[j]){
g[a[j]].pb(j);g[b[j]].pb(j);
}
}
//for(ll i=0;i<n;i++){cout<<i<<": "<<g[i]<<"\n";}
priority_queue<pip,vector<pip>,greater<pip>>pq;
pq.push({0,{0,-1}});
while(pq.size()){
pip x=pq.top();
// cout<<x<<"\n";
pq.pop();
if(pop[x.ss.ff]!=-2)continue;
pop[x.ss.ff]=x.ss.ss;
for(ll i :g[x.ss.ff]){
pq.push({x.ff+c[i],{a[i]^b[i]^x.ss.ff,i}});
}
}
vi rs;
ll pp=-1;
vector<int> vp;
while(t[i]){
vp.pb(pop[t[i]]);
if(t[i]^a[pop[t[i]]]^b[pop[t[i]]]==0)break;
if(zl[pop[t[i]]]){
if(pp!=-1)
pop2[pp]=zl[pop[t[i]]]-1;
pp=zl[pop[t[i]]]-1;
}
t[i]^=a[pop[t[i]]]^b[pop[t[i]]];
}
rev(vp);
//cout<<vp<<"\n";
answer(vp);
}
//cout<<v;
}
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define pb push_back
#define ff first
#define ss second
#define INF 1000000001LL
#define POT (1LL<<20)
#define INFL 1000000000000000099LL
#define pii pair<ll,ll>
#define ppi pair<pii,ll>
#define pip pair<ll,pii>
#define ppp pair<pii,pii>
#define vi vector<ll>
#define vii vector<pii>
#define vvi vector<vi>
#define al(x) x.begin(),x.end()
#define rev(x) reverse(al(x))
#define FCTCST 7
template<typename T, typename U>
pair<T, U> operator+(const pair<T, U>& a, const pair<T, U>& b) {
return {a.first + b.first, a.second + b.second};
}
template<typename T, typename U>
pair<T, U> operator-(const pair<T, U>& a, const pair<T, U>& b) {
return {a.first - b.first, a.second - b.second};
}
template<typename T, typename U,typename Z>
pair<T, U> operator*(const pair<T, U>& a, const Z& b) {
return {a.first*b, a.second*b};
}
template<typename T, typename U,typename Z>
pair<T, U> operator/(const pair<T, U>& a, const Z& b) {
return {a.first/b, a.second/b};
}
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os<<"{"<<p.ff<<", "<<p.ss<<"}";
return os;
}
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
os << "{";
for (size_t i = 0; i < v.size(); ++i) {
if (i) os << ", ";
os << v[i];
}
os << "}";
return os;
}
template<ll MOD=998244353>
struct mint_t{
ll x;
mint_t(ll y=0){x=y%MOD;if(x<0)x+=MOD;}
mint_t& operator+=(const mint_t& a){if((x+=a.x)>=MOD)x-=MOD;return *this;}
mint_t& operator-=(const mint_t& a){if((x+=MOD-a.x)>=MOD)x-=MOD;return *this;}
mint_t operator+(const mint_t& a)const{mint_t res(*this);return res+=a;}
mint_t operator-(const mint_t& a)const{mint_t res(*this);return res-=a;}
mint_t& operator*=(const mint_t& a){(x*=a.x)%=MOD;return *this;}
mint_t operator*(const mint_t& a)const{mint_t res(*this);return res*=a;}
mint_t fp(ll y)const{
mint_t a=1,b=x;
while(y){
if(y&1)a*=b;
b*=b;
y/=2;
}
return a;
}
mint_t& operator/=(const mint_t& a){(*this)*=a.fp(MOD-2);return *this;}
mint_t operator/(const mint_t& a)const{mint_t res(*this);return res/=a;}
};
#define mint mint_t<>
template<long long MOD>
istream& operator>>(istream& in, mint_t<MOD>& a){
ll x;
in>>x;
a=mint_t<MOD>(x);
return in;
}
template<long long MOD>
istream& operator<<(istream& out, mint_t<MOD>& a){
out<<a.x;
return out;
}
mint fct[FCTCST];
mint bnm(ll a,ll b){
if(b>a || a<0)return 0;
return fct[a]/fct[b]/fct[a-b];
}
ll pop[10007],pop2[300];
vi g[10007];
ll mj[16];
ll zl[20007];
bool vs2[10007];
string ms[300];
string to_bin(ll x,ll bt){
string rs;
while(bt--){rs.pb('0'+x%2);x/=2;}
rev(rs);return rs;
}
ll to_int(string s){
ll rs=0;
for(char c:s){
rs*=2;rs+=c-'0';
}
return rs;
}
std::string aoi(int n, int m, int q, int k, std::vector<int> a,
std::vector<int> b, std::vector<long long> c,
std::vector<int> t, std::vector<int> x){
for(ll i=0;i<k;i++)zl[x[i]]=i+1;
for(ll i=0;i<m;i++){
g[a[i]].pb(i);g[b[i]].pb(i);
}
for(ll i=0;i<n;i++)pop[i]=-2;
priority_queue<pip,vector<pip>,greater<pip>>pq;
pq.push({0,{0,-1}});
while(pq.size()){
pip x=pq.top();
pq.pop();
if(pop[x.ss.ff]!=-2)continue;
pop[x.ss.ff]=x.ss.ss;
for(ll i :g[x.ss.ff]){
pq.push({x.ff+c[i],{a[i]^b[i]^x.ss.ff,i}});
}
}
//for(ll i=0;i<n;i++)cout<<pop[i]<<" ";cout<<flush;
//cout<<"\n";
vvi v;
for(ll i=0;i<q;i++){
mj[i]=300;
ll x=t[i];
vi pm;
while(pop[x]!=-1){
if(zl[pop[x]]){pm.pb(zl[pop[x]]-1);
if(vs2[pop[x]]){pm.pop_back();
mj[i]=pop[x];break;
}
vs2[pop[x]]=1;
}
x^=a[pop[x]]^b[pop[x]];
}
v.pb(pm);
}
v.pb({});
for(ll i=0;i<k;i++)if(!vs2[i])v.back().pb(i);
//for(ll i=0;i<q;i++)cout<<mj[i]<<" ";
//cout<<v<<flush;
vii v2;
for(ll i=0;i<v.size();i++){
v2.pb({v[i].size(),i});
}
sort(al(v2));
ll mr1=v2[0].ss,mr2=v2[1].ss;
if(mr1>mr2)swap(mr1,mr2);
//cout<<mr1<<" "<<mr2<<"\n";
string rs="";
for(vi i:v)rs.pb('0');
rs[mr1]=rs[mr2]='1';
for(ll i=0;i<v.size();i++){
ll x=i;
if(x==mr2)x=mr1;
if(x>mr2)x--;
string pm=to_bin(x,4);
if(x==mr1){
pm.pb('0'+(i!=x));
}
for(ll j:v[i])ms[j]=pm;
}
for(ll i=0;i<k;i++)rs+=ms[i]+to_bin(mj[i],9);
//cout<<rs<<endl;
return rs;
}
void answer(const std::vector<int> &e);
string gt(string& st,ll x){
string rs;
//if(st.size()<x)cout<<"xd"<<flush;
for(ll i=0;i<x;i++)rs.pb(st[i]);
for(ll i=0;i<x;i++)st.erase(st.begin());
return rs;
}
void bitaro(int n, int m, int q, int k, std::vector<int> a, std::vector<int> b,
std::vector<long long> c, std::vector<int> t, std::vector<int> x,
std::string s){
for(ll i=0;i<k;i++)zl[x[i]]=i+1;
vvi v(q+1);
ll mr1=-1,mr2;
for(ll i=0;i<=q;i++){
ll x=to_int(gt(s,1));
if(x)if(mr1==-1)mr1=i;else mr2=i;
}
//cout<<mr1<<" "<<mr2<<"\n"<<flush;
for(ll i=0;i<k;i++){
ll x=to_int(gt(s,4));//cout<<x<<" "<<flush;
if(x>=mr2)x++;
if(x==mr1)if(to_int(gt(s,1)))x=mr2;
v[x].pb(i);
mj[i]=to_int(gt(s,9));
//cout<<"xd"<<flush;
}
//for(ll i=0;i<k;i++)cout<<mj[i]<<" ";cout<<"\n";
//cout<<v<<"\n";
for(ll i=0;i<k;i++)pop2[i]=300;
for(ll i=0;i<q;i++){
for(ll i=0;i<n;i++)pop[i]=-2;
for(ll j=0;j<n;j++)g[j].clear();
while(mj[i]!=300){
//cout<<mj[i]<<" "<<pop[mj[i]]<<" "<<x[mj[i]];return;
v[i].pb(x[mj[i]]);
mj[i]=pop2[mj[i]];
}
for(ll j:x)c[j]=1000000000000001LL;
for(ll j:v[i]){
g[a[x[j]]].pb(x[j]);
g[b[x[j]]].pb(x[j]);
c[x[j]]=0;
//cout<<x[j]<<" ";
}
for(ll j=0;j<m;j++){
if(!zl[j]){
g[a[j]].pb(j);g[b[j]].pb(j);
}
}
//for(ll i=0;i<n;i++){cout<<i<<": "<<g[i]<<"\n";}
priority_queue<pip,vector<pip>,greater<pip>>pq;
pq.push({0,{0,-1}});
while(pq.size()){
pip x=pq.top();
// cout<<x<<"\n";
pq.pop();
if(pop[x.ss.ff]!=-2)continue;
pop[x.ss.ff]=x.ss.ss;
for(ll i :g[x.ss.ff]){
pq.push({x.ff+c[i],{a[i]^b[i]^x.ss.ff,i}});
}
}
vi rs;
ll pp=-1;
vector<int> vp;
while(t[i]){
vp.pb(pop[t[i]]);
if(t[i]^a[pop[t[i]]]^b[pop[t[i]]]==0)break;
if(zl[pop[t[i]]]){
if(pp!=-1)
pop2[pp]=zl[pop[t[i]]]-1;
pp=zl[pop[t[i]]]-1;
}
t[i]^=a[pop[t[i]]]^b[pop[t[i]]];
}
rev(vp);
//cout<<vp<<"\n";
answer(vp);
}
//cout<<v;
}
