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;
const int UNDEF = -1;
const int INF = 1999999999;
const double EPS = 1e-9;
int n, d;
int main() {
  cin >> n >> d;
  int b[n];
  for (int i = 0; i < (n); ++i) {
    scanf("%d", b + i);
  }
  int ans = 0;
  for (int i = 1; i < (n); ++i) {
    int diff = b[i - 1] - b[i] + d;
    if (diff >= 0) {
      int p = diff / d;
      ans += p;
      b[i] += p * d;
    }
  }
  cout << ans << endl;
  return 0;
}
