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;
const long long int N = 1e9 + 100;
const int mod = 1e9 + 7, M = 2e3 + 100, se = 85 + 85;
int ans, a[M], b, c, d, n, m;
string s;
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
  cin >> n >> m;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 1; i < n; i++) {
    if (a[i] > a[i - 1]) continue;
    d = (a[i - 1] - a[i]) / m + 1;
    a[i] += d * m;
    ans += d;
  }
  cout << ans;
}
