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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  t = 1;
  while (t--) {
    long long n, d;
    cin >> n >> d;
    long long a[n];
    for (int i = 0; i < n; i++) cin >> a[i];
    long long count = 0;
    for (int i = 1; i < n; i++) {
      if (a[i] > a[i - 1])
        continue;
      else {
        count = count + (a[i - 1] - a[i]) / d + 1;
        a[i] = a[i] + ((a[i - 1] - a[i]) / d + 1) * d;
      }
    }
    cout << count << "\n";
  }
}
