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 n, d, v[1001000];
int main() {
  scanf("%d %d", &n, &d);
  for (int i = 0; i < n; i++) scanf("%d", &v[i]);
  int count = 0;
  while (1) {
    for (int i = 1; i < n; i++)
      if (v[i] <= v[i - 1]) {
        int aux = (v[i - 1] - v[i]);
        aux /= d;
        aux += 1;
        v[i] += (d * aux);
        count += aux;
      }
    bool stop = true;
    for (int i = 1; i < n; i++)
      if (v[i] <= v[i - 1]) stop = false;
    if (stop) break;
  }
  printf("%d\n", count);
  return 0;
}
