#include <bits/stdc++.h>
using namespace std;
#define int long long
int n,k,a[200005],tree[800020], dp[200005];
void update(int pos, int val, int id=1, int l=1, int r=n)
{
if (pos < l or r < pos) return;
if (l==r)
{
tree[id]=val;
return;
}
int mid=(l+r)/2;
update(pos,val,id*2,l,mid);
update(pos,val,id*2+1,mid+1,r);
tree[id]=min(tree[id*2],tree[id*2+1]);
}
int get(int val, int id=1, int l=1, int r=n)
{
if (tree[id] > val) return -1;
if (l==r) return l;
int mid=(l+r)/2;
int L = get(val,id*2,l,mid);
if (L != -1) return L;
return get(val,id*2+1,mid+1,r);
}
signed main()
{
fill(tree,tree+800000,1e6);
cin>>n>>k;
n+=2;
for (int i = 2; i < n; i++) cin>>a[i];
dp[n]=0;
update(n,a[n]-n*k);
for (int i = n-1; i > 0; i--)
{
// for (int i = 1; i <= 4*n; i++) cout<<tree[i]<<' ';cout<<endl;
int cur=get(a[i]-i*k);
dp[i]=dp[cur]+cur-i-1;
update(i,a[i]-i*k);
// cout<<cur<<' '<<dp[i]<<endl;
}
cout<<dp[1];
}
