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 n, d, ans;
  int b[2010];
  while (cin >> n >> d) {
    ans = 0;
    for (int i = 0; i < n; i++) {
      cin >> b[i];
      if (i >= 1 && b[i] <= b[i - 1]) {
        int x = b[i - 1] - b[i];
        b[i] += x / d * d;
        ans += x / d;
        while (b[i] <= b[i - 1]) {
          b[i] += d;
          ans++;
        }
      }
    }
    cout << ans << endl;
  }
  return 0;
}
