#include "dungeons.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> s,p,w,l;
int N;
vector<vector<pair<long long,int>>> lj;//lj[k][start] after 2^k play, {earn_hero,nxt};
vector<int> toN;// how many step to N if all wins;
void init(int i_n, vector<int> i_s, vector<int> i_p, vector<int> i_w, vector<int> i_l) {
N = i_n;
s = i_s, p = i_p, w = i_w, l = i_l;
lj = vector(30,vector<pair<long long,int>>(N));// atmost lost 2^24 times;
for(int i = 0;i < N;i++){
lj[0][i].first = p[i];
lj[0][i].second = l[i];
}
for(int k = 1;k < 30;k++){
for(int i = 0;i < N;i++){
auto [earn_hero,nxt] = lj[k-1][i];
auto [earn_hero2,nxt2] = lj[k-1][nxt];
lj[k][i] = {earn_hero+earn_hero2,nxt2};
}
}
toN = vector<int>(N+1,0);
for(int i = N-1;i >= 0;i--){
toN[i] = toN[w[i]]+1;
}
}
long long simulate(int x, int z) {
long long hero = z;
int cur = x;
for(int k = 29;k >= 0;k--){
auto [earn_hero,nxt] = lj[k][cur];
if(hero + earn_hero < s[0]) {
hero += earn_hero;
cur = nxt;
}
}
if(hero < s[0]){
auto [earn_hero,nxt] = lj[0][cur];
hero += earn_hero, cur = nxt;
}
hero += (long long)toN[cur]*s[0];
return hero;
}
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