#include <bits/stdc++.h>
#define fs first
#define se second
using namespace std;
typedef pair<int, int> pii;
const int inf = 1e9 + 1;
const int rinf = inf + inf;
const int linf = -1;
int n, l;
namespace LCT {
struct node {
int L, R, P;
int cnt, sum;
} ns[300010];
void set_cnt(int x, int v) {
ns[x].cnt = ns[x].sum = v;
}
void update(int x) {
ns[x].sum = ns[x].cnt;
if (ns[x].L) ns[x].sum += ns[ns[x].L].sum;
if (ns[x].R) ns[x].sum += ns[ns[x].R].sum;
}
bool is_root(int x) {
return ns[x].P == 0 || ns[ns[x].P].L != x && ns[ns[x].P].R != x;
}
void rotate(int x) {
int p = ns[x].P;
if (ns[p].L == x) {
ns[p].L = ns[x].R;
if (ns[p].L) ns[ns[p].L].P = p;
ns[x].R = p;
}
else {
ns[p].R = ns[x].L;
if (ns[p].R) ns[ns[p].R].P = p;
ns[x].L = p;
}
ns[x].P = ns[p].P;
ns[p].P = x;
if (ns[x].P) {
if (ns[ns[x].P].L == p) ns[ns[x].P].L = x;
else if (ns[ns[x].P].R == p) ns[ns[x].P].R = x;
}
update(p);
update(x);
}
void splay(int x) {
while (!is_root(x)) {
int p = ns[x].P;
if (!is_root(p)) {
if ((ns[ns[p].P].L == p) == (ns[p].L == x)) rotate(p);
else rotate(x);
}
rotate(x);
}
}
int access(int x) {
splay(x);
ns[x].R = 0;
update(x);
int ret = x;
while (ns[x].P) {
ret = ns[x].P;
splay(ret);
ns[ret].R = x;
update(ret);
splay(x);
}
return ret;
}
void link(int x, int p) {
access(x);
access(p);
ns[x].L = p;
ns[p].P = x;
update(x);
}
void cut(int x) {
access(x);
ns[ns[x].L].P = 0;
ns[x].L = 0;
update(x);
}
int get_sum(int x) {
access(x);
return ns[x].sum;
}
int par(int x) {
access(x);
x = ns[x].L;
while (ns[x].R) x = ns[x].R;
return x;
}
}
int pos[150010];
set<pii> sp;
int dl, dr;
void init(int N, int L, int X[]) {
n = N;
l = L;
dl = n + n + 1;
pos[n + 1] = linf - l;
dr = n + n + 2;
pos[n + 2] = rinf - l;
for (int i = 1; i <= n; ++i) {
LCT::set_cnt(i, 1);
pos[i] = X[i - 1];
sp.emplace(pos[i], i);
sp.emplace(pos[i] + l, i + n);
}
sp.emplace(linf, dl);
sp.emplace(rinf, dr);
pii prv = pii(-1, -1);
for (pii i : sp) {
if (prv.se != -1) {
if (prv.se <= n) {
LCT::link(prv.se, prv.se + n);
}
else {
LCT::link(prv.se, i.se);
}
}
prv = i;
}
}
int update(int p, int v) {
++p;
vector<int> need;
need.push_back(p + n);
auto it1 = prev(sp.find(pii(pos[p], p)));
auto it2 = prev(sp.find(pii(pos[p] + l, p + n)));
if (it1->se > n) need.push_back(it1->se);
if (it2->se > n) need.push_back(it2->se);
sp.erase(pii(pos[p], p));
sp.erase(pii(pos[p] + l, p + n));
pos[p] = v;
sp.emplace(pos[p], p);
sp.emplace(pos[p] + l, p + n);
auto it3 = prev(sp.find(pii(pos[p], p)));
auto it4 = prev(sp.find(pii(pos[p] + l, p + n)));
if (it3->se > n) need.push_back(it3->se);
if (it4->se > n) need.push_back(it4->se);
sort(need.begin(), need.end());
need.erase(unique(need.begin(), need.end()), need.end());
for (int i : need) LCT::cut(i);
for (int i : need) {
int x = pos[i - n] + l;
auto it = sp.upper_bound(pii(x, i));
int p = it->se;
LCT::link(i, p);
}
return LCT::get_sum(dl);
}
