#include <bits/stdc++.h>
#define FOR(i, l, r, x) for(int i = l; i <= r; i += x)
#define FOD(i, l, r, x) for(int i = l; i >= r; i -= x)
#define debug(x) cout << "[DEBUG]: " << #x << " = " << x << endl;
#define BIT(x) (1 << (x))
#define int long long
using namespace std;
const int N = 4e5 + 5;
const int mod = 1e9 + 7;
const int inf = 1e18;
struct SegmentTree {
int st[4 * N];
void upd(int id, int l, int r, int pos, int val) {
if (!(l <= pos && pos <= r)) return;
if (l == r) {
st[id] = val;
return;
}
int mid = (l + r) >> 1;
upd(id << 1, l, mid, pos, val);
upd(id << 1 | 1, mid + 1, r, pos, val);
st[id] = max(st[id << 1], st[id << 1 | 1]);
}
int get(int id, int l, int r, int u, int v) {
if (r < u || v < l) return -inf;
if (u <= l && r <= v) return st[id];
int mid = (l + r) >> 1;
return max(get(id << 1, l, mid, u, v),
get(id << 1 | 1, mid + 1, r, u, v));
}
};
int n, M, h[N];
inline bool isOn(int mask, int i) {
return ((mask >> i) & 1LL);
}
namespace sub1 {
void solve() {
int ans = 0;
FOR(mask, 0, BIT(n) - 1, 1) {
int last_i = -1;
bool isValid = true;
FOR(i, 0, n - 1, 1) {
if (!isOn(mask, i)) continue;
bool can_move = (h[last_i + 1] + ((i - last_i) * M) >= h[i + 1]);
if (!can_move) {
isValid = false;
break;
}
last_i = i;
}
if (isValid) {
ans = max(ans, (int)__builtin_popcountll(mask));
}
}
cout << n - ans << endl;
}
}
namespace sub2 {
int dp[N] = {};
inline bool isGreater(const int &i, const int &j) {
return ((h[j] + (i - j) * M) >= h[i]);
}
void solve() {
dp[0] = 1;
int ans = 1;
FOR(i, 0, n, 1) {
FOR(j, 0, i - 1, 1) {
if (isGreater(i, j)) {
if (dp[j] >= 1) dp[i] = max(dp[i], dp[j] + 1);
}
}
ans = max(ans, dp[i]);
}
//
// FOR(i, 0, n, 1) {
// cout << dp[i] << " ";
// }
// cout << '\n';
cout << n - ans + 1 << endl;
}
}
namespace sub4 {
SegmentTree st;
int a[N], dp[N];
vector <int> vec;
map <int, int> mp;
const int lim = 2e5 + 5;
void Compress() {
sort(begin(vec), end(vec));
vec.resize(unique(begin(vec), end(vec)) - begin(vec));
int id = 0;
for(const int &num : vec) {
// cout << num << '\n';
mp[num] = ++id;
}
FOR(i, 0, n, 1) {
a[i] = mp[a[i]];
}
}
void solve() {
vec.reserve(n + 5);
FOR(i, 0, n, 1) {
a[i] = h[i] - i * M;
vec.push_back(a[i]);
}
// FOR(i, 0, n, 1) {
// cout << a[i] << " ";
// }
// cout << '\n';
Compress();
dp[0] = 1;
int ans = 0;
//
////
// FOR(i, 0, n, 1) {
// cout << a[i] << " ";
// }
// cout << '\n';
// cout << '\n';
FOR(i, 0, n, 1) {
int val = a[i];
int dpj = st.get(1, 0, lim, val, lim);
if (dpj != 0) {
dp[i] = max(dp[i], dpj + 1);
}
st.upd(1, 0, lim, val, dp[i]);
ans = max(ans, dp[i]);
}
// FOR(i, 0, n, 1) {
// cout << dp[i] << " ";
// }
// cout << '\n';
cout << n - (ans - 1) << '\n';
}
}
void solve() {
cin >> n >> M;
FOR(i, 1, n, 1) cin >> h[i];
h[0] = 0;
if (n <= 20) {
sub1::solve();
} else if (n <= 5000) {
sub2::solve();
} else {
sub4::solve();
}
}
signed main() {
// freopen("random.inp", "r", stdin);
// freopen("sol2.out", "w", stdout);
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
solve();
}
