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;
long long int a[2005];
int main() {
  int n, i;
  long long int d, c = 0, dif;
  cin >> n >> d;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 0; i < n - 1; i++) {
    if (a[i + 1] <= a[i]) {
      dif = a[i] - a[i + 1] + 1;
      if (dif % d == 0) {
        a[i + 1] += dif;
        c += dif / d;
      } else {
        a[i + 1] += ((dif / d) + 1) * d;
        c += ((dif / d) + 1);
      }
    }
  }
  cout << c;
  return 0;
}
