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 main() {
  int n, d;
  while (cin >> n >> d) {
    int A[n], ans = 0;
    for (int i = 0; i < n; i++) cin >> A[i];
    for (int i = 1; i < n; i++) {
      if (A[i] <= A[i - 1]) {
        int rest = A[i - 1] - A[i], cnt = (rest / d) + 1;
        A[i] += cnt * d;
        ans += cnt;
      }
    }
    cout << ans << endl;
  }
  return 0;
}
