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, d;
  int data[2000];
  scanf("%d %d", &n, &d);
  for (int i = 0; i < n; i++) {
    scanf("%d", &data[i]);
  }
  int prev = data[0];
  int move = 0;
  for (int i = 1; i < n; i++) {
    if (data[i] <= prev) {
      int x = (prev - data[i]) / d + 1;
      data[i] += (d * x);
      move += x;
    }
    prev = data[i];
  }
  printf("%d\n", move);
  return 0;
}
