#include<bits/stdc++.h>
#include<random>
using namespace std;
using db=double;
using ll=long long;
using sll=__int128;//super long long
using lb=long double;//lb is slow
//numbers for hashing: b(19260817),mod(998244353)
// freopen("lasers.in", "r", stdin);
// freopen("lasers.out", "w", stdout);
class BinaryIndexedTree{
private:
vector<int>bit;
public:
BinaryIndexedTree(int n){
bit.resize(n+1);
}
void update(int index, int delta){
while(bit.size()>index){
bit[index]=min(bit[index],delta); index+=index&-index;
}
}
int query(int index){
int mx=1e9;
while(index>0){
mx=min(mx,bit[index]); index-=index&-index;
}
return mx;
}
};
int main(){
ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int n,m; cin>>n>>m; vector<int>a(n+1); map<int,vector<int>>mp;
for(int i=1; i<=n; i++){
cin>>a[i]; a[i]-=i*m; mp[a[i]].push_back(i);
}
mp[a[0]].push_back(0); vector<int>b(n+1); int count=n+1;
for(auto x:mp){
count--;
for(auto y:x.second){
b[y]=count;
}
}
BinaryIndexedTree BIT(n+1); vector<int>dp(n+1); int start=1;
while(a[start]-m>a[start-1] && start<=n){
a[start]=a[start-1]; start++;
}
for(int i=start; i<=n; i++){
dp[i]=i-1+BIT.query(b[i]);
BIT.update(b[i],dp[i]-i);
}
cout<<dp[n]+start-1<<'\n';
}
