#include"holiday.h"
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("O3")
// https://codeforces.com/blog/entry/103178?#comment-915863
struct Node {
long long sum;
int cnt;
int lCh, rCh;//children, indexes into `tree`
};
vector<Node> tree;
struct sum_kth_smallest {
vector<int> roots;
int mn, mx;
sum_kth_smallest(){}
sum_kth_smallest(const vector<int>& arr) : mn(INT_MAX), mx(INT_MIN), roots(arr.size() + 1, 0) {
tree.push_back({0, 0, 0}); //acts as null
for (int val : arr) mn = min(mn, val), mx = max(mx, val);
for (int i = 0; i < (int)arr.size(); i++)
roots[i + 1] = update(roots[i], mn, mx, arr[i]);
}
int update(int v, int tl, int tr, int idx) {
if (tl == tr) {
tree.push_back({tree[v].sum + tl, tree[v].cnt + 1, 0, 0});
return tree.size() - 1;
}
int tm = tl + (tr - tl) / 2;
int lCh = tree[v].lCh;
int rCh = tree[v].rCh;
if (idx <= tm)
lCh = update(lCh, tl, tm, idx);
else
rCh = update(rCh, tm + 1, tr, idx);
tree.push_back({tree[lCh].sum + tree[rCh].sum, tree[lCh].cnt + tree[rCh].cnt, lCh, rCh});
return tree.size() - 1;
}
/* find kth smallest number among arr[l], arr[l+1], ..., arr[r]
* k is 1-based, so find_kth(l,r,1) returns the min
*/
int query(int l, int r, int k) const {
// assert(1 <= k && k <= r - l + 1); //note this condition implies L <= R
// assert(0 <= l && r + 1 < (int)roots.size());
return query(roots[l], roots[r + 1], mn, mx, k);
}
int query(int vl, int vr, int tl, int tr, int k) const {
if (tl == tr)
return tl;
int tm = tl + (tr - tl) / 2;
int left_count = tree[tree[vr].lCh].cnt - tree[tree[vl].lCh].cnt;
if (left_count >= k) return query(tree[vl].lCh, tree[vr].lCh, tl, tm, k);
return query(tree[vl].rCh, tree[vr].rCh, tm + 1, tr, k - left_count);
}
/* find **sum** of k smallest numbers among arr[l], arr[l+1], ..., arr[r]
* k is 1-based, so find_kth(l,r,1) returns the min
*/
long long query_sum(int l, int r, int k) const {
if(k<=0)return 0;
k=min(k, (r-l+1));
if(l>r)return 0;
// assert(1 <= k && k <= r - l + 1); //note this condition implies L <= R
// assert(0 <= l && r + 1 < (int)roots.size());
return query_sum(roots[l], roots[r + 1], mn, mx, k);
}
long long query_sum(int vl, int vr, int tl, int tr, int k) const {
if (tl == tr)
return 1LL * tl * k;
int tm = tl + (tr - tl) / 2;
int left_count = tree[tree[vr].lCh].cnt - tree[tree[vl].lCh].cnt;
long long left_sum = tree[tree[vr].lCh].sum - tree[tree[vl].lCh].sum;
if (left_count >= k) return query_sum(tree[vl].lCh, tree[vr].lCh, tl, tm, k);
return left_sum + query_sum(tree[vl].rCh, tree[vr].rCh, tm + 1, tr, k - left_count);
}
};
sum_kth_smallest sg;
int n, start, d;
vector<int> attraction;
vector<long long> F, S, F2, S2;
long long get(int l, int r, int k) {
return -sg.query_sum(l, r, k);
}
void calcf1(int l, int r, int pl, int pr) {
if(l>r)return;
int mid = (l+r)/2;
long long res=0;
int opt = pl;
for(int i = pl;i<=pr;i++) {
long long val = get(start, i, mid-abs(i-start));
if(val >= res) {
res=val;
opt=i;
}
}
F[mid] = res;
calcf1(l, mid-1, pl, opt);
calcf1(mid+1, r, opt, pr);
}
void calcs1(int l, int r, int pl, int pr) {
if(l>r)return;
int mid = (l+r)/2;
long long res=0;
int opt = pl;
for(int i = pl;i<=pr;i++) {
long long val = get(start, i, mid-2*abs(i-start));
if(val >= res) {
res=val;
opt=i;
}
}
S[mid] = res;
calcs1(l, mid-1, pl, opt);
calcs1(mid+1, r, opt, pr);
}
//
void calcf2(int l, int r, int pl, int pr) {
if(l>r)return;
int mid = (l+r)/2;
long long res=0;
int opt = pl;
for(int i = pl;i<=pr;i++) {
long long val = get(i, start-1, mid-abs(i-start));
if(val >= res) {
res=val;
opt=i;
}
}
F2[mid] = res;
calcf2(l, mid-1, opt, pr);
calcf2(mid+1, r, pl, opt);
}
void calcs2(int l, int r, int pl, int pr) {
if(l>r)return;
int mid = (l+r)/2;
long long res=0;
int opt = pl;
for(int i = pl;i<=pr;i++) {
long long val = get(i,start-1, mid-2*abs(i-start));
if(val >= res) {
res=val;
opt=i;
}
}
S2[mid] = res;
calcs2(l, mid-1, opt, pr);
calcs2(mid+1, r, pl, opt);
}
long long int findMaxAttraction(int _n, int _start, int _d, int _attraction[]) {
n=_n;
start=_start;
d=_d;
S.resize(d+1);
F.resize(d+1);
S2.resize(d+1);
F2.resize(d+1);
attraction=vector<int>(_attraction, _attraction+_n);
for(int &i:attraction)i*=-1;
sg=sum_kth_smallest(attraction);
for(int &i:attraction)i*=-1;
calcf1(1, _d, _start, _n-1);
calcs1(1, _d, _start, _n-1);
calcf2(1, _d, 0, _start-1);
calcs2(1, _d, 0, _start-1);
long long res=0;
for(int i = 0;i<=d;i++) {
res=max(res, F[i]+S2[d-i]);
res=max(res, S[i]+F2[d-i]);
}
return res;
}
