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;
long long int a[10005];
int main() {
  long int i, j, k, n, l = 0, d;
  cin >> n >> d;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 1; i < n; i++) {
    if (a[i] <= a[i - 1]) {
      k = a[i - 1] - a[i];
      if (k < d)
        l++, a[i] += d;
      else {
        j = ceil(double(k / (double)d));
        l += j;
        a[i] += j * d;
        if (a[i] <= a[i - 1]) a[i] += d, l++;
      }
    }
  }
  cout << l << endl;
  return 0;
}
