#pragma GCC optimize ("unroll-loops")
#pragma GCC optimize ("Ofast")
#include <bits/stdc++.h>
#include "elephants.h"
using namespace std;
const int MAXN = 2e5 + 10;
const int INF = 1e9;
const int B = 1500; // :(
const int UPD = 387;
int x[MAXN], ind[MAXN];
pair<int, int> suf[MAXN];
set<pair<int, int>> s;
vector<vector<pair<int, int>>> buckets;
int n, l;
int cnt_upd = 0;
void process(int id){
auto &b = buckets[id];
if(b.empty()) return;
int sz = (int) b.size();
int r = sz - 1;
for(int i=(sz - 1); i>=0; i--){
while(b[r].first - b[i].first > l) r--;
int last = 0;
if(r < sz - 1) last = suf[b[r + 1].second].first;
int extra = (b[i].first + l) - b[sz - 1].first;
if(r < sz - 1) extra = suf[b[r + 1].second].second;
suf[b[i].second] = {last + 1, extra};
}
}
void create_buckets(){
int cnt = 0;
buckets.clear();
buckets.push_back({});
for(auto x : s){
if(cnt < B){
buckets.back().push_back(x);
cnt ++;
} else{
buckets.push_back({x});
cnt = 1;
}
ind[x.second] = (int) buckets.size() - 1;
}
for(int i=0; i<(int) buckets.size(); i++) process(i);
}
void refresh(){
cnt_upd ++;
if(cnt_upd == UPD){
create_buckets();
cnt_upd = 0;
}
}
int find_bucket(int x){
for(int i=0; i<(int) buckets.size(); i++){
if(!buckets[i].empty() && x <= buckets[i].back().first){
return i;
}
}
return (int) buckets.size() - 1;
}
void remove(int id){
int j = ind[id];
for(int i=0; i<buckets[j].size(); i++){
if(buckets[j][i].second == id){
buckets[j].erase(buckets[j].begin() + i);
break;
}
}
s.erase({x[id], id});
process(j);
}
void add(int id){
int j = find_bucket(x[id]);
ind[id] = j;
for(int i=0; i<buckets[j].size(); i++){
if(x[id] < buckets[j][i].first){
buckets[j].insert(buckets[j].begin() + i, {x[id], id});
break;
}
}
if(buckets[j].empty() || x[id] >= buckets[j].back().first){
buckets[j].push_back({x[id], id});
}
s.insert({x[id], id});
process(j);
}
int query(){
int ans = 0;
int cur = s.begin()->second;
while(true){
ans += suf[cur].first;
int nxt = buckets[ind[cur]].back().first + suf[cur].second;
auto pos = s.upper_bound({nxt, INF});
if(pos == s.end()) break;
cur = pos->second;
}
return ans;
}
void init(int n_, int l_, int x_[]){
n = n_;
l = l_;
cnt_upd = 0;
for(int i=0; i<n; i++) x[i] = x_[i];
s.clear();
for(int i=0; i<n; i++) s.insert({x[i], i});
create_buckets();
}
int update(int id, int y){
remove(id);
x[id] = y;
add(id);
refresh();
return query();
}
