#include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int N;
long long H;
cin >> N >> H;
vector<long long> S(N);
for (int i = 0; i < N; i++) cin >> S[i];
/*
We maintain a valid interval [low, high] for the current stack height.
Initially, for the first stack, it must be exactly S[0].
*/
long long low = 0, high = 0;
/*
Two heaps are used:
- leftHeap : max-heap, stores candidates near the upper side
- rightHeap : min-heap, stores candidates near the lower side
Together they help us "pull" heights back into the allowed interval
with minimum number of cube add/remove operations.
*/
priority_queue<long long> leftHeap;
priority_queue<long long, vector<long long>, greater<long long>> rightHeap;
// Total number of operations (adding/removing cubes)
long long operations = 0;
// Initialize using the first stack
leftHeap.push(S[0]);
rightHeap.push(S[0]);
for (int i = 1; i < N; i++) {
/*
When moving from stack i-1 to i,
the allowed height range expands by H on both sides.
*/
low += H;
high += H;
long long currentHeight = S[i];
/*
Case 1:
Current stack is TOO LOW to satisfy |S[i] - S[i-1]| ≤ H
→ we must ADD cubes
*/
if (leftHeap.top() > currentHeight + low) {
long long required = leftHeap.top() - (currentHeight + low);
operations += required;
// Adjust heaps to reflect the forced increase
leftHeap.push(currentHeight + low);
rightHeap.push(leftHeap.top() - low - high);
leftHeap.pop();
}
/*
Case 2:
Current stack is TOO HIGH
→ we must REMOVE cubes
*/
else if (rightHeap.top() < currentHeight - high) {
long long required = (currentHeight - high) - rightHeap.top();
operations += required;
// Adjust heaps to reflect the forced decrease
rightHeap.push(currentHeight - high);
leftHeap.push(rightHeap.top() + low + high);
rightHeap.pop();
}
/*
Case 3:
Current stack already lies in the safe interval
→ no operations needed
*/
else {
leftHeap.push(currentHeight + low);
rightHeap.push(currentHeight - high);
}
}
cout << operations << "\n";
return 0;
}
