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;
long long a[100500];
int d;
int n;
long long ans = 0;
int main() {
  scanf("%d %d", &n, &d);
  for (int i = 0; i < n; i++) {
    int x;
    scanf("%d", &x);
    a[i] = x;
  }
  long long prev = -(1 << 30);
  for (int i = 0; i < n; i++) {
    if (a[i] <= prev) {
      long long dist = (prev + 1 - a[i]);
      long long cnt = (dist + d - 1) / d;
      ans += cnt;
      prev = a[i] + cnt * d;
    } else {
      prev = a[i];
    }
  }
  printf("%d", ans);
  return 0;
}
