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;
int main() {
  int n, d;
  cin >> n >> d;
  vector<int> s;
  s.resize(n);
  for (int i = 0; i < n; i++) cin >> s[i];
  int count = 0;
  for (int i = 1; i < n; i++) {
    if (s[i] <= s[i - 1]) {
      double c = (s[i - 1] - s[i]) / (d * 1.0);
      if (int(c) < c)
        c += ((int(c) + 1) - c);
      else
        c++;
      s[i] += d * c;
      count += c;
    }
  }
  cout << count;
  return 0;
}
