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
from math import ceil


n, d = map(int, input().split())
sequence = [int(i) for i in input().split()]
count = 0
for i in range(1, n):
    if sequence[i] <= sequence[i - 1]:
        if not (sequence[i - 1] - sequence[i]) % d:
            count1 = (sequence[i - 1] - sequence[i]) // d + 1
        else:
            count1 = ceil((sequence[i - 1] - sequence[i]) / d)
        if not count1:
            sequence[i] += d
            count += 1
        else:
            sequence[i] += d * count1
            count += count1
print(count)
