#include "dungeons.h"
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define vec vector
const int MXN = 50'050;
const int LOGN = 30;
const int LOGS = 30;
struct Data {
int mnt;
int sum;
int32_t v;
};
Data binjmps[LOGS][MXN][LOGN];
int n;
vec<int32_t> s;
vec<int32_t> p;
vec<int32_t> w;
vec<int32_t> l;
const int MXS = 1e15+100;
void init(int32_t n_i, std::vector<int32_t> s_i, std::vector<int32_t> p_i, std::vector<int32_t> w_i, std::vector<int32_t> l_i) {
// preprocessing fill in binjmps
s = s_i;
s.push_back(0);
p = p_i;
w = w_i;
w.push_back(n_i);
l = l_i;
n = n_i;
for(int i = 0; i<LOGS; i++) {
for(int j = 0; j<=n; j++) {
if(s[j] > (1<<i)) {
binjmps[i][j][0] = {s[j], p[j], l[j]};
}
else {
binjmps[i][j][0] = {MXS, s[j], w[j]};
}
}
for(int k = 1; k<LOGN; k++) {
for(int j = 0; j<=n; j++) {
auto nxt = &binjmps[i][binjmps[i][j][k-1].v][k-1];
auto me = &binjmps[i][j][k-1];
int nxt_mnt = (nxt->mnt == MXS) ? MXS : (nxt->mnt-min(me->sum, (int)nxt->mnt));
binjmps[i][j][k] = {min(me->mnt, nxt_mnt), me->sum+nxt->sum, nxt->v};
assert(binjmps[i][j][k].sum >= 0);
}
}
}
return;
}
long long simulate(int32_t u, int32_t z) {
int cur_s = z;
for(int32_t i = 0; i<LOGS; i++) {
//cerr << u << ' ' << cur_s << '\n';
for(int32_t j = LOGN-1; j>=0; j--) {
if(binjmps[i][u][j].mnt > cur_s) {
cur_s += binjmps[i][u][j].sum;
u = binjmps[i][u][j].v;
}
}
}
assert(cur_s > 0);
cerr << cur_s << '\n';
return cur_s;
}
