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;
const long long INF = 1e9 + 10;
const long long MOD = 1e9 + 7;
const long long P = 239017;
const long long BINF = 1e18 + 10;
inline void source() {
  long long n, k, prevv = 0, ans = 0;
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) {
    long long a;
    cin >> a;
    long long l = 0, r = 1e6 + 10;
    while (r - l > 1) {
      long long mid = (r + l) / 2;
      if (a + mid * k > prevv) {
        r = mid;
      } else {
        l = mid;
      }
    }
    while (a + l * k <= prevv) {
      l++;
    }
    prevv = a + l * k;
    ans += l;
  }
  cout << ans;
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  srand(time(0));
  source();
  return 0;
}
