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 arr[10000];
  int n, la;
  int ans = 0;
  cin >> la >> n;
  for (int i = 0; i < la; i++) {
    cin >> arr[i];
  }
  int diff;
  for (int i = 1; i < la; i++) {
    if (arr[i] <= arr[i - 1]) {
      diff = arr[i - 1] - arr[i];
      if (diff == 0) {
        arr[i] += n;
        ans++;
      }
      if (diff > 0) {
        int k = diff / n + 1;
        arr[i] += n * k;
        ans += k;
      }
    }
  }
  cout << ans;
}
