#include "elephants.h"
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx,avx2,fma")
using namespace std;
typedef long long ll;
typedef pair<int, int> pi;
#define MAX 150010
#define INF 1000000010
#define B 300
int N;
int L;
int arr[MAX];
int cnt;
map<int, int> ncnt;
int gcnt;
set<int> allv;
vector<pair<int, pi>> bukkit[MAX];
inline bool cmpp(const pair<int, pi>& p1, const pair<int, pi>& p2) {
return p1.first < p2.first;
}
//refresh bukkit
void refb(int b) {
if (bukkit[b].empty()) return;
while (bukkit[b].size() && bukkit[b].back().first == INF) bukkit[b].pop_back();
int i;
int ub = bukkit[b].size();
for (i = bukkit[b].size() - 1; i >= 0; i--) {
int x = bukkit[b][i].first;
int e = x + L;
while (ub && bukkit[b][ub - 1].first > e) ub--;
if (ub == bukkit[b].size()) bukkit[b][i].second = pi(1, e);
else bukkit[b][i].second = pi(bukkit[b][ub].second.first + 1, bukkit[b][ub].second.second);
}
}
void ref() {
for (int i = 0; i < gcnt; i++) bukkit[i].clear();
gcnt = 0;
for (auto v : allv) {
if (bukkit[gcnt].size() == B) gcnt++;
bukkit[gcnt].push_back(make_pair(v, pi(0, 0)));
}
gcnt++;
for (int i = 0; i < gcnt; i++) refb(i);
}
int calc() {
int en = -2, i;
int cnt = 0;
for (i = 0; i < gcnt; i++) {
if (bukkit[i].empty()) continue;
auto ub = lower_bound(bukkit[i].begin(), bukkit[i].end(), make_pair(en + 1, pi(0, 0)), cmpp) - bukkit[i].begin();
if (ub == bukkit[i].size()) continue;
cnt += bukkit[i][ub].second.first;
en = bukkit[i][ub].second.second;
}
return cnt;
}
void init(int N, int L, int X[]) {
::N = N;
::L = L;
int i;
for (i = 0; i < N; i++) arr[i] = X[i], allv.insert(arr[i]), ncnt[arr[i]]++;
ref();
}
int update(int i, int y) {
cnt++;
if (cnt == B) ref(), cnt = 0;
int x = arr[i];
arr[i] = y;
ncnt[x]--;
if (ncnt[x] == 0) {
int i, ind = 0;
for (i = 0; i < gcnt; i++) if (bukkit[i].size() && bukkit[i].begin()->first <= x) ind = i;
int it = lower_bound(bukkit[ind].begin(), bukkit[ind].end(), make_pair(x, pi(0, 0)), cmpp) - bukkit[ind].begin();
bukkit[ind].erase(bukkit[ind].begin() + it);
allv.erase(x);
refb(ind);
}
if (ncnt[y] == 0) {
allv.insert(y);
int i, ind = 0;
for (i = 0; i < gcnt; i++) if (bukkit[i].size() && bukkit[i].begin()->first <= y) ind = i;
int nind;
nind = lower_bound(bukkit[ind].begin(), bukkit[ind].end(), make_pair(y, pi(0, 0))) - bukkit[ind].begin();
bukkit[ind].insert(bukkit[ind].begin() + nind, make_pair(y, pi(0, 0)));
allv.insert(y);
refb(ind);
}
ncnt[y]++;
return calc();
}
