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;
template <class T>
void minimize(T& a, const T& b) {
  a = min(a, b);
}
template <class T>
void maximize(T& a, const T& b) {
  a = max(a, b);
}
int main() {
  int n, d;
  cin >> n >> d;
  long long p = 0;
  long long ans = 0;
  for (int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    long long b = max(0LL, (p + 1) - a);
    long long k = (b + d - 1) / d;
    p = a + d * k;
    ans += k;
  }
  cout << ans << endl;
}
