#include <bits/stdc++.h>
#define debug(x) cerr << #x << " " << x << "\n"
#define debugs(x) cerr << #x << " " << x << " "
using namespace std;
typedef long long ll;
typedef pair <ll, ll> pii;
const ll NMAX = 200005;
const ll VMAX = 26;
const ll INF = (1LL << 55);
const ll MOD = 90000000000000001;
const ll BLOCK = 1000000;
const ll base = 1000000001;
const ll nr_of_bits = 18;
ll v[NMAX];
int dp[NMAX];
vector <int> nrm;
unordered_map <int, int> mp;
int aint[NMAX * 4];
void update(int node, int st, int dr, int a, int b){
if(st == dr){
aint[node] = min(aint[node], b);
return;
}
int mid = (st + dr) / 2;
if(a <= mid)
update(node * 2, st, mid, a, b);
else
update(node * 2 + 1, mid + 1, dr, a, b);
aint[node] = min(aint[node * 2], aint[node * 2 + 1]);
}
int query(int node, int st, int dr, int a, int b){
if(a <= st && dr <= b)
return aint[node];
int mid = (st + dr) / 2;
int minim = 2e9;
if(a <= mid)
minim = min(minim, query(node * 2, st, mid, a, b));
if(b > mid)
minim = min(minim, query(node * 2 + 1, mid + 1, dr, a, b));
return minim;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int n, i, m;
for(i = 1; i < NMAX * 4; i++)
aint[i] = 2e9;
cin >> n >> m;
nrm.push_back(0);
nrm.push_back(-2e9);
for(i = 2; i <= n + 1; i++){
cin >> v[i];
v[i] -= m * (i - 1);
nrm.push_back(v[i]);
}
sort(nrm.begin(), nrm.end());
int cnt = 0;
for(i = 0; i < nrm.size(); i++){
if(i == 0 || nrm[i] != nrm[i - 1])
cnt++;
mp[nrm[i]] = cnt;
}
for(i = 1; i <= n + 1; i++)
v[i] = mp[v[i]];
n += 2;
v[n] = 1; /// numar artificial
int minim = 0;
for(i = 1; i <= n; i++){
dp[i] = i - 1 + query(1, 1, NMAX, v[i], NMAX);
if(i == 1)
dp[i] = 0;
update(1, 1, NMAX, v[i], dp[i] - i);
}
cout << dp[n];
return 0;
}
