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 n, d;
long long tmp, ans;
long long a[2005];
inline void read(long long &x) {
  long long f;
  char c;
  for (f = 1, c = getchar(); c < '0' || c > '9'; c = getchar())
    if (c == '-') f = -1;
  for (x = 0; c <= '9' && c >= '0'; c = getchar()) x = x * 10 + (c & 15);
  x *= f;
}
int main() {
  read(n);
  read(d);
  for (int i = 1; i <= n; i++) read(a[i]);
  for (int i = 2; i <= n; i++) {
    if (a[i] > a[i - 1]) continue;
    tmp = (a[i - 1] - a[i]) / d + 1;
    ans += tmp;
    a[i] += tmp * d;
  }
  printf("%lld\n", ans);
  return 0;
}
