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 v[2009];
int main() {
  int n, d, ans = 0, t;
  scanf("%d%d%d", &n, &d, &v[0]);
  for (int i = 1; i < n; i++) {
    scanf("%d", &v[i]);
    if (v[i - 1] >= v[i]) {
      t = ceil((double)(v[i - 1] + 1 - v[i]) / (double)d);
      ans += t;
      v[i] += t * d;
    }
  }
  printf("%d\n", ans);
  return 0;
}
