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;
long long s[1000005];
int main(void) {
  int n, d, ans = 0;
  cin >> n >> d >> s[1];
  for (int i = 2; i <= n; ++i) {
    cin >> s[i];
    int cnt = 0;
    if (s[i] <= s[i - 1]) cnt = (s[i - 1] - s[i] + d) / d;
    s[i] += cnt * d;
    ans += cnt;
  }
  return cout << ans << '\n', 0;
}
