#include "dungeons.h"
#include <vector>
#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
os<<"{";
for(auto e:v)os<<e<<",";
return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
os<<t<<" ";
dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
if(i)os<<",";
os<<get<i>(t);
print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
os<<"{";
print_tuple<0,tuple<Args...>,Args...>(os,t);
return os<<"}";
}
template<class t>
void print(t x,int suc=1){
cout<<x;
if(suc==1)
cout<<"\n";
if(suc==2)
cout<<" ";
}
ll read(){
ll i;
cin>>i;
return i;
}
vi readvi(int n,int off=0){
vi v(n);
rep(i,n)v[i]=read()+off;
return v;
}
pi readpi(int off=0){
int a,b;cin>>a>>b;
return pi(a+off,b+off);
}
template<class t,class u>
void print(const pair<t,u>&p,int suc=1){
print(p.a,2);
print(p.b,suc);
}
template<class T>
void print(const vector<T>&v,int suc=1){
rep(i,v.size())
print(v[i],i==int(v.size())-1?suc:2);
}
template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
rep(i,v.size())
print(v[i]+off,i==int(v.size())-1?suc:2);
}
template<class T,size_t N>
void print(const array<T,N>&v,int suc=1){
rep(i,N)
print(v[i],i==int(N)-1?suc:2);
}
string readString(){
string s;
cin>>s;
return s;
}
template<class T>
T sq(const T& t){
return t*t;
}
//#define CAPITAL
void yes(bool ex=true){
#ifdef CAPITAL
cout<<"YES"<<"\n";
#else
cout<<"Yes"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void no(bool ex=true){
#ifdef CAPITAL
cout<<"NO"<<"\n";
#else
cout<<"No"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void possible(bool ex=true){
#ifdef CAPITAL
cout<<"POSSIBLE"<<"\n";
#else
cout<<"Possible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void impossible(bool ex=true){
#ifdef CAPITAL
cout<<"IMPOSSIBLE"<<"\n";
#else
cout<<"Impossible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
constexpr ll ten(int n){
return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
return __builtin_popcount(t);
}
int popcount(ll t){
return __builtin_popcountll(t);
}
bool ispow2(int i){
return i&&(i&-i)==i;
}
ll mask(int i){
return (ll(1)<<i)-1;
}
bool inc(int a,int b,int c){
return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
sort(all(v));
v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
#ifdef LOCAL
static mt19937_64 gen;
#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
return uniform_int_distribution<ll>(l, r)(gen);
}
template<class t>
void myshuffle(vc<t>&a){
rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
return lower_bound(all(v),a)-v.bg;
}
vvc<int> readGraph(int n,int m){
vvc<int> g(n);
rep(i,m){
int a,b;
cin>>a>>b;
//sc.read(a,b);
a--;b--;
g[a].pb(b);
g[b].pb(a);
}
return g;
}
vvc<int> readTree(int n){
return readGraph(n,n-1);
}
//N() が単位元
//VERIFY: yosupo
//CF407E
template<class N>
struct segtree{
vc<N> x;
int s;
segtree(){}
template<class t>
segtree(vc<t> a){
int n=a.size();
s=1;
while(s<n){s*=2;}
x.resize(s*2);
rep(i,n)
x[s+i]=N(a[i]);
gnr(i,1,s)
x[i]=N::merge(x[i*2],x[i*2+1]);
}
//NOT Verified
segtree(int n){
resize(n);
}
void resize(int n){
s=1;
while(s<n){s*=2;}
x.assign(s*2,N());
gnr(i,1,s)
x[i]=N::merge(x[i*2],x[i*2+1]);
}
void set(int i,const N&t){
i+=s;
x[i]=t;
while(i>>=1)x[i]=N::merge(x[i*2],x[i*2+1]);
}
N composite(int b,int e){
assert(b<=e);
N lf,rt;
for(int l=b+s,r=e+s;l<r;l>>=1,r>>=1){
if (l&1){
lf=N::merge(lf,x[l]);
l++;
}
if (r&1){
r--;
rt=N::merge(x[r],rt);
}
}
return N::merge(lf,rt);
}
N getall(){
return x[1];
}
//UTPC2020E
//n 超えるかもしれない
template <class F,class... Args>
pair<int,N> max_right(int l,F f,Args&&... args){
assert(0<=l&&l<=s);
if(l==s)return mp(s,N());
l+=s;
N sm;
assert((sm.*f)(forward<Args>(args)...));
do {
while (l % 2 == 0) l >>= 1;
if (!(N::merge(sm,x[l]).*f)(forward<Args>(args)...)){
while (l < s) {
l = (2 * l);
N tmp=N::merge(sm,x[l]);
if ((tmp.*f)(forward<Args>(args)...)) {
sm = tmp;
l++;
}
}
return mp(l - s,sm);
}
sm = N::merge(sm, x[l]);
l++;
} while ((l & -l) != l);
return mp(s,sm);
}
//UTPC2020E
template <class F,class... Args>
pair<int,N> min_left(int r,F f,Args&&... args){
assert((N().*f)(forward<Args>(args)...));
assert(0<=r&&r<=s);
if(r==0)return mp(0,N());
r+=s;
N sm;
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!(N::merge(x[r],sm).*f)(forward<Args>(args)...)) {
while (r < s) {
r = (2 * r + 1);
N tmp=N::merge(x[r],sm);
if ((tmp.*f)(forward<Args>(args)...)) {
sm = tmp;
r--;
}
}
return mp(r + 1 - s,sm);
}
sm = N::merge(x[r], sm);
} while ((r & -r) != r);
return mp(0,sm);
}
};
struct N{
int sum,mn;
N(pi v=pi(0,inf)):sum(v.a),mn(v.b){}
static N merge(const N&a,const N&b){
return N(pi(a.sum+b.sum,min(a.mn-b.sum,b.mn)));
}
bool ok(int v){
return mn>v;
}
};
const int L=26;
struct Solver{
int n,ord;
vvc<int> t;
vi sub,par,in,head,jp,ni;
vc<pi> ls;
vc<N> acc;
segtree<N> seg;
vc<pi> es;
vi deg;
void ae(int v,int p){
//t[p].pb(v);
es.eb(v,p);
deg[p]++;
sub[p]+=sub[v];
assert(par[v]==-1);
par[v]=p;
}
void dfs(int v,int h,N w){
in[v]=ord++;
head[v]=h;
acc[v]=N::merge(w,acc[v]);
for(auto&to:t[v]){
if(sub[to]>sub[t[v][0]])
swap(to,t[v][0]);
}
for(auto to:t[v]){
dfs(to,to==t[v][0]?h:to,to==t[v][0]?acc[v]:N(pi(0,inf)));
}
}
void init(int nn,vi to,vi add,vi need,vc<pi> lls){
n=nn;
ord=0;
add.pb(0);
need.pb(0);
t.resize(n+1);
sub.resize(n+1,1);
par.resize(n+1,-1);
in.resize(n+1,-1);
head.resize(n+1,-1);
jp.resize(n+1,-1);
ni.resize(n+1,-1);
ls=lls;
ls.eb(0,-1);
acc.resize(n+1);
es.reserve(n);
deg.resize(n+1);
{
vi cnt(n+1);
rep(i,n)cnt[to[i]]++;
vi qbuf;qbuf.reserve(n+1);
rep(i,n+1)if(cnt[i]==0)qbuf.pb(i);
rep(idx,si(qbuf)){
int v=qbuf[idx];
if(v<n){
int p=to[v];
ae(v,p);
if(--cnt[p]==0)qbuf.pb(p);
}
}
rep(i,n)if(cnt[i]){
int x=i;
while(1){
assert(cnt[x]==1);
cnt[x]=0;
int y=to[x];
if(y!=i){
ae(x,y);
x=y;
}else{
jp[x]=y;
break;
}
}
}
}
rep(i,n+1)t[i].resize(deg[i]);
for(auto [v,p]:es)t[p][--deg[p]]=v;
rep(i,n+1)acc[i]=N(pi(add[i],need[i]));
rep(r,n+1)if(par[r]==-1)dfs(r,r,N(pi(0,inf)));
vc<pi> rw(n+1);
rep(i,n+1){
ni[in[i]]=i;
rw[in[i]]=pi(add[i],need[i]);
}
seg=segtree<N>(rw);
vi().swap(sub);
vc<pi>().swap(es);
vi().swap(deg);
}
pi work(int x,int z){
assert(acc[x].mn<=z);
auto [i,w]=seg.min_left(in[x]+1,&N::ok,z);
z+=w.sum;
x=ni[i-1];
z+=ls[x].a;
x=ls[x].b;
return pi(x,z);
}
pi slv(int x,int z){
while(1){
if(acc[x].mn<=z)return work(x,z);
int h=head[x];
z+=acc[x].sum;
if(par[h]==-1){
x=jp[h];
break;
}else{
x=par[h];
}
}
dmp(par);
dmp(jp);
N cur(pi(0,inf));
while(1){
dmp(x);
cur=N::merge(acc[x],cur);
int h=head[x];
if(par[h]==-1){
x=jp[h];
break;
}else{
x=par[h];
}
}
if(cur.mn>=z){
z+=(cur.mn-z+cur.sum-1)/cur.sum*cur.sum;
}
while(1){
dmp(x);
if(acc[x].mn<=z)return work(x,z);
int h=head[x];
z+=acc[x].sum;
assert(par[h]!=-1);
x=par[h];
}
}
} ss[L];
void init(signed n, std::vector<signed> s, std::vector<signed> p, std::vector<signed> w, std::vector<signed> l) {
rep(lv,L){
vi to(n),add(n),need(n,inf);
vc<pi> ls(n);
rep(i,n){
if(s[i]<=mask(lv)){
to[i]=w[i];
add[i]=s[i];
}else{
to[i]=l[i];
add[i]=p[i];
need[i]=s[i];
}
ls[i]=pi(s[i],w[i]);
}
ss[lv].init(n,to,add,need,ls);
}
}
long long simulate(signed x,signed z_){
int z=z_;
while(x!=-1){
int lv=min(topbit(z),L-1);
tie(x,z)=ss[lv].slv(x,z);
}
return z;
}
