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() {
  long long int i, j, k, l, m, n, d = 0;
  scanf("%lld %lld", &m, &n);
  long long int a[m];
  for (i = 0; i < m; i++) {
    scanf("%lld", &a[i]);
  }
  for (i = 0; i < m; i++) {
    if (a[i] >= a[i + 1]) {
      l = (a[i] - a[i + 1]);
      if (l % n == 0) {
        j = (l / n) + 1;
        d = d + j;
        a[i + 1] = a[i + 1] + n * j;
      } else {
        k = (l / n) + 1;
        d = d + k;
        a[i + 1] = a[i + 1] + n * k;
      }
    }
  }
  printf("%lld\n", d);
}
