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 int po[1005][10];
vector<int> primes;
using ll = long long int;
using dl = double;
int main() {
  ios_base::sync_with_stdio(false);
  string ptr, str, uni;
  ll n, i, j, p = 2, m, after, a, mark, ans = 0, array[10000], guest;
  vector<ll> cv;
  set<ll> sc;
  cin >> n >> m;
  for (i = 0; i < n; i++) {
    cin >> array[i];
  }
  for (i = 1; i < n; i++) {
    if (array[i] < array[i - 1]) {
      ll dif = array[i - 1] - array[i];
      mark = dif / m;
      if (dif % m != 0) mark++;
      ans += mark;
      array[i] = array[i] + mark * m;
    }
    if (array[i] == array[i - 1]) {
      array[i] = array[i] + m;
      ans++;
    }
  }
  cout << ans << endl;
}
