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
# https://codeforces.com/problemset/problem/11/A
# 900

import math

n, d = map(int, input().split())
l = list(map(int, input().split()))

m = 0
for i in range(n):
    if i > 0:
        if l[i-1] >= l[i]:
            _m = math.ceil(((l[i-1]+1) - l[i]) / d)
            m += _m
            l[i] += _m * d

print(m)