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>
using namespace std;
int N, D;
int main() {
  int i, a, b, res = 0;
  scanf("%d%d", &N, &D);
  scanf("%d", &a);
  for (i = 1; i < N; i++) {
    scanf("%d", &b);
    if (b <= a) {
      int d = (a - b) / D + 1;
      b += d * D;
      res += d;
    }
    a = b;
  }
  printf("%d", res);
  return 0;
}
