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
a = raw_input().split()
n = int(a[0])
m = int(a[1])
ans = 0
a = raw_input().split()
for i in range(n):
    a[i] = int(a[i])
    if i > 0 and a[i - 1] >= a[i]:
        t = (a[i - 1] - a[i]) / m + 1
        a[i] += t * m
        ans += t
print ans
