#include "dungeons.h"
#include <vector>
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
typedef pair<int32_t, ll> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi, ll> pii;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define maxn 400010
#define maxb1 61
#define maxb2 20
#define INF (ll)1e18
#define MOD 1000000007
typedef pair <vi, int> pvi;
typedef pair <int,pi> ipi;
typedef vector <pii> vpii;
pi dp[maxn][maxb1]; // (ending node, added val) if start at i and do 2^k steps winning if 2^j >= S
int mx[maxn][maxb1]; // max z for dp[i][j][k] to be accurate
int num[maxn][maxb1];
int S[maxn], P[maxn], W[maxn], L[maxn];
int N;
bool vis[maxn];
inline int msb(int x){
return 63 - __builtin_clzl(x);
}
void dfs(int i,int j){
//cerr << i << ' ' << j << '\n';
if (dp[i][j] != pi(-1,-1)) return;
vis[i] = 1;
int nxt, add;
if (i == N) nxt = N, add = 0;
else if ((1LL << j) >= S[i]) nxt = W[i], add = S[i];
else nxt = L[i], add = P[i];
if (!vis[nxt]){
dfs(nxt, j);
}else{
dp[i][j] = pi(nxt,add); num[i][j] = 1;
return;
}
if (num[nxt][j] == num[dp[nxt][j].f][j]){
dp[i][j] = dp[dp[nxt][j].f][j];
dp[i][j].s += add + dp[nxt][j].s;
mx[i][j] = min(mx[nxt][j] - add, mx[dp[nxt][j].f][j] - add - dp[nxt][j].s);
if (S[i] > (1LL << j)) mx[i][j] = min(mx[i][j], S[i]);
num[i][j] = num[nxt][j] * 2 + 1;
}else dp[i][j] = pi(nxt, add), mx[i][j] = (S[i] > (1LL << j) ? S[i] : INF), num[i][j] = 1;
}
void init(int32_t n, std::vector<int32_t> s, std::vector<int32_t> p, std::vector<int32_t> w, std::vector<int32_t> l) {
N = n;
FOR(i,0,N-1){
S[i] = s[i], P[i] = p[i], W[i] = w[i], L[i] = l[i];
}
FOR(i,1,N) FOR(j,0,maxb1-1) dp[i][j] = pi(-1,-1);
FOR(j,0,maxb1-1){
FOR(i,1,N) vis[i] = 0;
dp[N][j] = pi(N, 0);
FOR(i,1,N) dfs(i,j);
}
/*
FOR(i,0,N-1) FOR(j,0,maxb1-1){
if ((1 << j) >= S[i]) dp[i][j][0] = pi(W[i], S[i]);
else dp[i][j][0] = pi(L[i], P[i]);
if (S[i] > (1 << j)) mx[i][j][0] = S[i] - 1;
else mx[i][j][0] = INF;
}
FOR(j,0,maxb1-1) dp[N][j][0] = pi(N, 0);
FOR(k,1,maxb2-1) FOR(j,0,maxb1-1){
FOR(i,0,N){
dp[i][j][k] = dp[dp[i][j][k-1].f][j][k-1];
dp[i][j][k].s += dp[i][j][k-1].s;
mx[i][j][k] = min(mx[i][j][k-1], mx[dp[i][j][k-1].f][j][k-1] - dp[i][j][k-1].s);
}
}
*/
return;
}
long long simulate(int32_t x, int32_t _z) {
ll z = _z;
while (1){
//cout << msb(z) << ' ';
//cout << x << ' ';
int a = msb(z);
while (z < mx[x][msb(z)]){
pi val = dp[x][msb(z)];
z += val.s;
x = val.f;
}
/*
DEC(k,maxb2-1,0) if (z <= mx[x][msb(z)][k] && dp[x][msb(z)][k].f < N){
pi val = dp[x][msb(z)][k];
z += val.s;;
x = val.f;
}
*/
//cout << x << ' ';
//cout << x << ' ' << z << '\n';
if (z >= S[x] && W[x] == N) return z + S[x];
if (z < S[x] && L[x] == N) return z + P[x];
//cout << z << ' ';
if (z >= S[x]){
z += S[x];
x = W[x];
}else{
z += P[x];
x = L[x];
}
//cout << x << ' ';
//cout << zz << ' ' << z << '\n';
//assert(msb(z) >= a+1);
}
return 0;
}
