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() {
  long long int N, D, X, prev = -1, cnt = 0;
  cin >> N >> D >> prev;
  for (long long int i = (0); i < (N - 1); ++i) {
    cin >> X;
    if (X <= prev) {
      cnt += max((int)ceil((prev - X) / (double)D), 1);
      X += max((int)ceil((prev - X) / (double)D), 1) * D;
      if (X == prev) {
        X += D;
        cnt++;
      }
    }
    prev = X;
  }
  cout << cnt << endl;
  return 0;
}
