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() {
  int g, a, x = 0, c;
  int bilangan[2001];
  while (scanf("%d", &g) != EOF) {
    x = 0;
    scanf("%d", &a);
    for (int i = 0; i < g; i++) {
      scanf("%d", &bilangan[i]);
      if (bilangan[i - 1] >= bilangan[i] && i > 0) {
        c = (bilangan[i - 1] - bilangan[i]) / a + 1;
        bilangan[i] = bilangan[i] + (c * a);
        x += c;
      }
    }
    printf("%d", x);
    printf("\n");
  }
}
