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>
typedef struct pair {
  int x, y;
} pair;
int const N = 20000;
int i, j, k, s, n, m, d, t;
int arr[N];
int main() {
  scanf("%d %d", &n, &d);
  for (i = 1; i <= n; i++) {
    scanf("%d", &arr[i]);
  }
  for (i = 1; i < n; i++) {
    if (arr[i] >= arr[i + 1]) {
      t = (arr[i] - arr[i + 1]) / d + 1;
      arr[i + 1] += t * d;
      s += t;
    }
  }
  printf("%d", s), puts("");
  return 0;
}
