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 main() {
  int n, d, b[2000], i, k, count;
  while (scanf("%d %d", &n, &d) == 2) {
    for (i = 0; i < n; i++) scanf("%d", &b[i]);
    count = 0;
    for (i = 1; i < n; i++) {
      if (b[i] <= b[i - 1]) {
        k = (b[i - 1] - b[i]) / d + 1;
        b[i] += k * d;
        count += k;
      }
    }
    printf("%d\n", count);
  }
  return 0;
}
