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 argc, char const *argv[]) {
  int x, b;
  cin >> x >> b;
  int a[x], k[x];
  for (int i = 0; i < x; ++i) {
    cin >> a[i];
    k[i] = a[i];
  }
  int ans = 0;
  for (int i = 1; i < x; ++i) {
    if (a[i] <= a[i - 1]) {
      int r = (a[i - 1] - a[i]) / b + 1;
      a[i] += r * b;
      ans += r;
    }
  }
  cout << ans << "\n";
}
