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