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 arr[2003];
int main() {
  int n, d, i, c;
  scanf("%d%d", &n, &d);
  for (i = 0; i < n; i++) scanf("%d", &arr[i]);
  c = 0;
  for (i = 1; i < n; i++) {
    if (arr[i] <= arr[i - 1]) {
      if ((arr[i - 1] + 1 - arr[i]) % d == 0) {
        c += (arr[i - 1] + 1 - arr[i]) / d;
        arr[i] = arr[i - 1] + 1;
      } else {
        c += (arr[i - 1] + 1 - arr[i]) / d + 1;
        arr[i] += ((arr[i - 1] + 1 - arr[i]) / d + 1) * d;
      }
    }
  }
  printf("%d\n", c);
  return 0;
}
