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>
int main() {
  int n;
  scanf("%d", &n);
  int d;
  scanf("%d", &d);
  int i;
  long int a[2000];
  for (i = 0; i < n; i++) {
    scanf("%ld", &a[i]);
  }
  int x = 0;
  for (i = 1; i < n; i++) {
    if (a[i] <= a[i - 1]) {
      int xi = ceil((a[i - 1] - a[i]) / d);
      a[i] += xi * d;
      int k = 0;
      while (a[i - 1] >= a[i]) {
        k++;
        a[i] += k * d;
      }
      xi += k;
      x += xi;
    }
  }
  printf("%d", x);
  return 0;
}
