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 d, n, b[2000], m = 0, i;
  cin >> n >> d;
  for (i = 0; i < n; i++) {
    cin >> b[i];
  }
  if (d > 1) {
    for (i = 0; i < n - 1; i++) {
      while (b[i + 1] <= b[i]) {
        b[i + 1] += d;
        m++;
      }
    }
  } else {
    for (i = 0; i < n - 1; i++) {
      if (b[i + 1] <= b[i]) {
        m += (b[i] - b[i + 1]) + 1;
        b[i + 1] = b[i] + 1;
      }
    }
  }
  cout << m;
  return 0;
}
