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>
int Step() {
  int n, d;
  std::cin >> n;
  std::cin >> d;
  if (n < 2 || d < 1) {
    return 0;
  }
  int* seq = new int[n];
  for (int i = 0; i < n; i++) {
    std::cin >> seq[i];
  }
  int step = 0;
  for (int i = 1; i < n; i++) {
    if (seq[i] - seq[i - 1] <= 0) {
      int stem = (seq[i - 1] - seq[i]) / d;
      seq[i] += d * (stem);
      if (seq[i] - seq[i - 1] <= 0) {
        stem += 1;
        seq[i] += d;
      }
      step += stem;
    }
  }
  return step;
}
int main() { std::cout << Step(); }
