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 execute() {
  int n, d, diff, amount;
  cin >> n >> d;
  int a[n], i, cnt = 0;
  for (i = 0; i < n; i++) cin >> a[i];
  for (i = 1; i < n; i++) {
    if (a[i] < a[i - 1]) {
      diff = a[i - 1] - a[i];
      amount = diff / d + (bool)((double)diff / (double)d);
      cnt += amount;
      a[i] += amount * d;
    } else if (a[i] == a[i - 1])
      cnt++, a[i] += d;
  }
  cout << cnt << endl;
  return 0;
}
char mtest = false;
unsigned short TE = 1;
int main() {
  ios_base::sync_with_stdio(false);
  if (mtest) cin >> TE;
  while (TE--) execute();
  return 0;
}
