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() {
  long long a = 0, b = 0, c, n, t;
  cin >> n >> t;
  vector<long long> p;
  for (long long i = 0; i < n; i++) {
    cin >> c;
    p.push_back(c);
  }
  a = 0;
  for (long long i = 1; i < n; i++) {
    if (p[i] == p[i - 1]) {
      a++;
      p[i] = p[i - 1] + t;
    } else if (p[i - 1] > p[i]) {
      b = p[i - 1] - p[i];
      a = a + (b / t) + 1;
      p[i] = p[i] + (t * ((b / t) + 1));
    }
  }
  cout << a << endl;
}
