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>
#pragma comment(linker, "/STACK:100000000")
using namespace std;
const double PI = acos(-1.0);
const int INF = 1e9;
const int MOD = INF + 7;
const double EPS = 1e-9;
const long long BIGINF = 1e17;
mt19937 rng(time(0));
uniform_int_distribution<int> uid(0, INF / 2);
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, d, x, p, res = 0;
  cin >> n >> d >> p;
  for (int i = 1; i < n; ++i) {
    cin >> x;
    if (x > p)
      p = x;
    else {
      res += (p - x + d) / d;
      p = x + ((p - x + d) / d) * d;
    }
  }
  cout << res << '\n';
  return 0;
}
