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
import math

n, d = map(int, input().split())
a = list(map(int, input().split()))
total = 0
last = a[0]
for i in range(1, n):
    num = a[i]
    if a[i] > last:
        last = a[i]
    else:
        move = math.ceil((last - a[i] + 1) / d)
        last = num + move * d
        total += move
    # print(num, total, last)
print(total)
