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
def strictly_increasing(sequence):
    return all(x < y for x, y in zip(seq, seq[1:]))


def is_equal(sequence):
    return all(x == y for x, y in zip(seq, seq[1:]))


n, d = map(int, input().split())
seq = list(map(int, input().split()))
count = 0
if strictly_increasing(seq):
    print(0)
else:
    for i in range(len(seq)-1):
        if seq[i] > seq[i+1]:
            number = seq[i] - seq[i+1]
            number2 = d*(number // d)
            if number % d != 0:
                number2 += d
            seq[i+1] += number2
            count += number2//d
        if seq[i] == seq[i+1]:
            seq[i+1] += d
            count += 1
    print(count)





