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 d, a[2004], n;
  cin >> n >> d;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  int res = 0;
  for (int i = 2; i <= n; i++) {
    if (a[i] <= a[i - 1]) {
      int t = (a[i - 1] - a[i]) / d;
      a[i] += (t + 1) * d;
      res += t + 1;
    }
  }
  cout << res;
}
