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 s, d, count = 0, num = 0;
  cin >> s >> d;
  int arr[s];
  for (int i = 0; i < s; i++) {
    cin >> arr[i];
  }
  for (int j = 0; j < s - 1; j++) {
    if (arr[j] >= arr[j + 1]) {
      num = ((arr[j] - arr[j + 1]) / d) + 1;
      arr[j + 1] = arr[j + 1] + d * num;
      count = count + num;
    }
  }
  cout << count;
}
