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;
  while (~scanf("%d%d", &n, &d)) {
    int time = 0, fir, sec, temp;
    scanf("%d", &fir);
    for (int i = 2; i <= n; i++) {
      scanf("%d", &sec);
      if (fir > sec) {
        temp = (fir - sec) / d + 1;
        time += temp;
        sec += temp * d;
      } else if (fir == sec)
        time++, sec += d;
      fir = sec;
    }
    printf("%d\n", time);
  }
  return 0;
}
