// When we're in drama,
// there's that person over there
// polishing their skill.
// 抗えぬ運命と決まっているのなら
// 私はあなたの為に生きたい
// 誰かの為に生きてこその人生
// 輝を増すこと知っているから
// Zanite's template
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
// Pragmas
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// Namespaces
using namespace std;
using namespace __gnu_pbds;
// Data types
using si = short int;
using ll = long long;
using ull = unsigned long long;
using lll = __int128;
using ld = long double;
// Pairs
using pii = pair<int, int>;
using psi = pair<si, si>;
using pll = pair<ll, ll>;
using plll = pair<lll, lll>;
using pld = pair<ld, ld>;
#define fi first
#define se second
// PBDS
template<typename Z>
using ordered_set = tree<Z, null_type, less<Z>, rb_tree_tag, tree_order_statistics_node_update>;
// Quick macro functions
#define sqr(x) ((x)*(x))
#define debug(x) cout << #x << " = " << (x) << '\n'
#define debugV(v, x) cout << #v << "[" << (x) << "] = " << (v[x]) << '\n'
#define rrebug(x) cerr << #x << " = " << (x) << '\n'
#define rrebugV(v, x) cerr << #v << "[" << (x) << "] = " << (v[x]) << '\n'
#define All(x) x.begin(), x.end()
#define Sort(x) sort(All(x))
#define Reverse(x) reverse(All(x))
#define Uniqueify(x) Sort(x); x.erase(unique(All(x)), x.end())
#define RandomSeed chrono::steady_clock::now().time_since_epoch().count()
#define MultipleTestcases int _tc; cin >> _tc; for (int _cur_tc = 1; _cur_tc <= _tc; _cur_tc++)
// Check min and max
template<typename Z> bool chmin(Z &a, Z b) {return (b < a) ? a = b, true : false;}
template<typename Z> bool chmax(Z &a, Z b) {return (b > a) ? a = b, true : false;}
// Other constants
const ll INF = 1e18;
const ll iINF = 1e9;
const ld EPS = 1e-9;
const ld iEPS = 1e-6;
pll operator+(const pll &a, const pll &b) {
return make_pair(a.fi + b.fi, a.se + b.se);
}
pll operator-(const pll &a, const pll &b) {
return make_pair(a.fi - b.fi, a.se - b.se);
}
const ull LARGE = 1'000'000'000'000'001; // 1e15 + 1
ull cnt(ull x) {return x / LARGE;}
ull val(ull x) {return x % LARGE;}
class PersistentSegtree {
private:
int n, ptr, sz;
struct P {
ull val = 0;
int l, r;
};
vector<P> node;
vector<int> root;
int newNode() {
node.emplace_back();
return ptr++;
}
int copyNode(int idx) {
node.push_back(node[idx]);
return ptr++;
}
int build(int l, int r) {
int idx = newNode();
if(l == r)
return idx;
node[idx].l = build(l, (l + r) / 2);
node[idx].r = build((l + r) / 2 + 1, r);
return idx;
}
int update(int idx, int l, int r, int x, ull val) {
idx = copyNode(idx);
if(l == r) {
node[idx].val += val;
return idx;
}
int mid = (l + r) / 2;
if(x <= mid)
node[idx].l = update(node[idx].l, l, mid, x, val);
else
node[idx].r = update(node[idx].r, mid + 1, r, x, val);
node[idx].val = node[node[idx].l].val + node[node[idx].r].val;
return idx;
}
ull query(int idxl, int idxr, int l, int r, int x, int y) {
if(y < l || r < x)
return 0;
if(x <= l && r <= y)
return node[idxr].val - node[idxl].val;
int mid = (l + r) / 2;
return query(node[idxl].l, node[idxr].l, l, mid, x, y)
+ query(node[idxl].r, node[idxr].r, mid + 1, r, x, y);
}
ull search(int idx, int l, int r, ull x) {
if (cnt(node[idx].val) <= x) return val(node[idx].val);
if (l == r) return 0;
int mid = (l + r) / 2;
if (cnt(node[node[idx].l].val) >= x) {
return search(node[idx].l, l, mid, x);
} else {
return val(node[node[idx].l].val) + search(node[idx].r, mid + 1, r, x - cnt(node[node[idx].l].val));
}
}
public:
PersistentSegtree(int _n) : n(_n), ptr(0) {
sz = 30 * n;
node.reserve(sz);
root.push_back(build(1, n));
}
void update(int x, ull val) {
root.push_back(update(root.back(), 1, n, x, val));
}
ull query(int l, int r, int x, int y) {
return query(root[l - 1], root[r], 1, n, x, y);
}
ull search(int i, int x) {
return search(root[i], 1, n, x);
}
};
const int maxN = 100'023;
int N, start, D;
ll A[maxN];
vector<ll> getOpt(vector<ll> &P, int mult) {
int K = P.size();
vector<pll> compress;
for (int i = 0; i < K; i++) {
compress.push_back({P[i], i});
}
sort(All(compress), greater<pll>());
vector<int> idx(K);
for (int i = 0; i < K; i++) {
idx[compress[i].se] = i + 1;
}
// Compute "convex hull"
PersistentSegtree PS(K);
for (int i = 0; i < K; i++) {
PS.update(idx[i], (ull)P[i] + LARGE);
}
auto get = [&](int consider, int t) {
int tk = t - mult * (consider + 1);
if (tk <= 0) {
return 0ll;
}
ll ans = PS.search(consider + 1, tk);
// cout << "get " << consider << " " << t << ": " << ans << "\n";
// cout << "search(" << consider << ", " << tk << ") = " << ans << "\n";
return ans;
};
auto get_isect = [&](int i, int j) {
int l = j, r = 3*K, ans = -1;
while (l <= r) {
int m = (l + r) / 2;
if (get(j, m) > get(i, m)) {
ans = m;
r = m - 1;
} else {
l = m + 1;
}
}
return ans;
};
vector<int> CH = {0};
vector<int> isect;
for (int i = 1; i < K; i++) {
int cur_isect = get_isect(CH.back(), i);
if (cur_isect == -1) continue;
bool push = true;
while (CH.size() >= 2) {
cur_isect = get_isect(CH.back(), i);
if (cur_isect == -1) {
push = false;
break;
}
if (cur_isect <= isect.back()) {
CH.pop_back();
isect.pop_back();
} else break;
}
if (push) {
isect.push_back(get_isect(CH.back(), i));
CH.push_back(i);
}
}
// debug(CH);
// debug(isect);
int cs = CH.size();
vector<ll> ret;
for (int i = 0, ptr = 0; i <= 3*K; i++) {
while ((ptr < cs-1) && (i >= isect[ptr])) ptr++;
ret.push_back(get(CH[ptr], i));
}
// debug(ret);
// cout << "===\n";
return ret;
}
ll findMaxAttraction(int N, int start, int D, int attraction[]) {
for (int i = 1; i <= N; i++) A[i] = attraction[i-1];
D = min(D, 3*N);
start++;
vector<ll> L, R;
for (int i = start-1; i >= 0; i--) L.push_back(A[i]);
for (int i = start+1; i <= N+1; i++) R.push_back(A[i]);
// debug(L); debug(R);
ll ans = 0;
for (int tl = 1; tl <= 2; tl++) {
int tr = 3 - tl;
vector<ll> optL = getOpt(L, tl);
vector<ll> optR = getOpt(R, tr);
while ((int)optL.size() <= D) optL.push_back(optL.back());
while ((int)optR.size() <= D) optR.push_back(optR.back());
// debug(optL); debug(optR);
// don't visit attraction at start
for (int i = 0; i <= D; i++) {
chmax(ans, optL[i] + optR[D - i]);
}
// visit attraction at start
for (int i = 0; i <= D-1; i++) {
chmax(ans, optL[i] + optR[D-1 - i] + A[start]);
}
}
return ans;
}
// あなたの傍に居させて...
// dibisakan
