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 w[2005];
int main(void) {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, d;
  long long ans = 0;
  cin >> n >> d;
  for (int i = 1; i <= n; i++) cin >> w[i];
  for (int i = 2; i <= n; i++) {
    if (w[i] < w[i - 1])
      ans += (w[i - 1] - w[i] + d - 1) / d,
          w[i] += (w[i - 1] - w[i] + d - 1) / d * d;
    if (w[i] == w[i - 1]) ans++, w[i] += d;
  }
  cout << ans;
  return 0;
}
