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;
int main() {
  int n, d, next, cnt = 0, now, i, diff;
  scanf("%d%d", &n, &d);
  scanf("%d", &now);
  for (i = 1; i < n; i++) {
    scanf("%d", &next);
    if (next <= now) {
      diff = (now - next) / d + 1;
      next += diff * d;
      cnt += diff;
    }
    now = next;
  }
  printf("%d\n", cnt);
}
