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
n, d = map(lambda x: int(x), raw_input().split())
b = map(lambda x: int(x), raw_input().split())

a = b[:]
count = 0

for i in range(1, n):
    if b[i] <= a[i-1]:
        dif = a[i-1] - b[i]
        a[i] += d * (dif / d)
        count += dif / d
        while a[i] <= a[i-1]:
            a[i] += d
            count += 1
print count    
