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>
int main() {
  long N, A, B, D, S = 0, X;
  scanf("%ld%ld%ld", &N, &D, &A);
  while (--N) {
    scanf("%ld", &B);
    if (B <= A) {
      X = (A - B);
      X = (X + D) / D;
      S += X;
      B += (X * D);
    }
    A = B;
  }
  printf("%ld", S);
  return 0;
}
