#include "candies.h"
#include <vector>
#include <algorithm>
#include <tuple>
#define pii pair<int, int>
#define ff first
#define ss second
using namespace std;
const long long INF = (long long)8e18 + 100;
struct Node
{
long long mx, mn, up, dn, l;
Node(void) : mx(0), mn(0), up(0), dn(0), l(0) {}
}seg[808080];
void prop(int ind)
{
if(!seg[ind].l) return;
seg[ind << 1].mx += seg[ind].l;
seg[ind << 1].mn += seg[ind].l;
seg[ind << 1].l += seg[ind].l;
seg[ind << 1 | 1].mx += seg[ind].l;
seg[ind << 1 | 1].mn += seg[ind].l;
seg[ind << 1 | 1].l += seg[ind].l;
seg[ind].l = 0;
}
void mrge(int ind)
{
Node &nd = seg[ind], &x = seg[ind << 1], &y = seg[ind << 1 | 1];
nd.mx = max(x.mx, y.mx);
nd.mn = min(x.mn, y.mn);
nd.up = max({x.up, y.up, y.mx - x.mn});
nd.dn = max({x.dn, y.dn, x.mx - y.mn});
}
void upd(int ind, int s, int e, int l, int r, long long x)
{
if(e <= l || r <= s) return;
if(l <= s && e <= r)
{
seg[ind].mn += x;
seg[ind].mx += x;
seg[ind].l += x;
return;
}
int mid = s + e >> 1;
prop(ind);
upd(ind << 1, s, mid, l, r, x);
upd(ind << 1 | 1, mid, e, l, r, x);
mrge(ind);
}
int ub(int ind, int s, int e, long long x, long long mx)
{
if(s + 1 == e)
{
if(mx - seg[ind].mn > x) return s;
else return s - 1;
}
int mid = s + e >> 1;
prop(ind);
if(seg[ind << 1 | 1].up > x || mx - seg[ind << 1 | 1].mn > x) return ub(ind << 1 | 1, mid, e, x, mx);
else return ub(ind << 1, s, mid, x, max(mx, seg[ind << 1 | 1].mx));
}
int lb(int ind, int s, int e, long long x, long long mn)
{
if(s + 1 == e)
{
if(seg[ind].mx - mn > x) return s;
else return s - 1;
}
int mid = s + e >> 1;
prop(ind);
if(seg[ind << 1 | 1].dn > x || seg[ind << 1 | 1].mx - mn > x) return lb(ind << 1 | 1, mid, e, x, mn);
else return lb(ind << 1, s, mid, x, min(mn, seg[ind << 1 | 1].mn));
}
long long xqry(int ind, int s, int e, int l, int r)
{
if(e <= l || r <= s) return -INF;
if(l <= s && e <= r) return seg[ind].mx;
int mid = s + e >> 1;
prop(ind);
return max(xqry(ind << 1, s, mid, l, r), xqry(ind << 1 | 1, mid, e, l, r));
}
long long nqry(int ind, int s, int e, int l, int r)
{
if(e <= l || r <= s) return INF;
if(l <= s && e <= r) return seg[ind].mn;
int mid = s + e >> 1;
prop(ind);
return min(nqry(ind << 1, s, mid, l, r), nqry(ind << 1 | 1, mid, e, l, r));
}
vector<int> distribute_candies(vector<int> c, vector<int> l, vector<int> r, vector<int> v)
{
int n = c.size();
int T = l.size();
vector<pii> ls[n + 1];
for(int i = 0; i < T; ++i)
{
ls[l[i]].push_back({i + 1, v[i]});
ls[r[i] + 1].push_back({i + 1, -v[i]});
}
long long sum = 0;
long long pr = 0;
vector<int> ans;
for(int i = 0; i < n; ++i)
{
for(auto [p, x] : ls[i]) upd(1, 0, T + 2, p + 1, T + 2, x), sum += x;
upd(1, 0, T + 2, 1, T + 2, -c[i] - 1 - pr);
pr = -c[i] - 1;
int a = ub(1, 0, T + 2, c[i], -INF);
int b = lb(1, 0, T + 2, c[i], INF);
if(a > b) ans.push_back(-xqry(1, 0, T + 2, a, T + 2) + sum - 1);
else ans.push_back(-nqry(1, 0, T + 2, b, T + 2) - c[i] + sum - 1);
}
return ans;
}
