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;
const int M = 3000;
const int N = 300000;
const double eps = 1e-6;
int a[M];
int n, d;
int main() {
  while (scanf("%d%d", &n, &d) == 2) {
    int cnt = 0;
    for (int i(0); i < (n); i++) {
      scanf("%d", &a[i]);
      if (i) {
        if (a[i] <= a[i - 1]) {
          int temp = (a[i - 1] - a[i]) / d + 1;
          a[i] += temp * d;
          cnt += temp;
        }
      }
    }
    printf("%d\n", cnt);
  }
  return 0;
}
