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() {
  long n(0), d(0);
  scanf("%ld %ld\n", &n, &d);
  long current(-1), total(0);
  for (int k = 0; k < n; k++) {
    long temp(0);
    scanf("%ld", &temp);
    if (current < temp) {
      current = temp;
    } else {
      long times = 1 + (current - temp) / d;
      current = temp + times * d;
      total += times;
    }
  }
  printf("%ld\n", total);
  return 0;
}
