A sequence a0, a1, ..., at - 1 is called increasing if ai - 1 < ai for each i: 0 < i < t.

You are given a sequence b0, b1, ..., bn - 1 and a positive integer d. In each move you may choose one element of the given sequence and add d to it. What is the least number of moves required to make the given sequence increasing?

Input

The first line of the input contains two integer numbers n and d (2 ≤ n ≤ 2000, 1 ≤ d ≤ 106). The second line contains space separated sequence b0, b1, ..., bn - 1 (1 ≤ bi ≤ 106).

Output

Output the minimal number of moves needed to make the sequence increasing.

Examples

Input

4 2
1 3 3 2


Output

3
#include <bits/stdc++.h>
using namespace std;
const long long N = 2e5 + 5;
const int dx[4] = {0, 0, 1, -1};
const int dy[4] = {1, -1, 0, 0};
int x[4], y[4];
void solve() {
  int n, d, ans = 0;
  cin >> n >> d;
  vector<int> v(n);
  for (int i = 0; i < n; i++) cin >> v[i];
  for (int i = 1; i < n; i++) {
    if (v[i - 1] < v[i])
      continue;
    else {
      int r = (v[i - 1] - v[i]) / d + 1;
      v[i] += (1ll * d * r);
      ans += r;
    }
  }
  cout << ans << endl;
  return;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  solve();
  return 0;
}
