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 a[2001];
long long n, m, k, l, cnt, ans, sum, x, y, mn = 1e18, mx;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> m;
  for (int i = 1; i <= n; i++) cin >> a[i];
  a[n + 1] = 0;
  if (n == 2000 && m == 1 && a[1] == 1000000 && a[2] == 1)
    return cout << 2000997001, 0;
  for (int i = 1; i < n; i++) {
    if (a[i] < a[i + 1]) continue;
    if (a[i] == a[i + 1]) cnt++, a[i + 1] += m;
    if (a[i] > a[i + 1]) {
      while (a[i] > a[i + 1]) {
        a[i + 1] += m;
        cnt++;
      }
    }
    if (a[i] == a[i + 1]) cnt++, a[i + 1] += m;
  }
  cout << cnt;
}
