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 getint():
    raw = raw_input().split()
    return [int(x) for x in raw]

last = -1
count = 0;
t, d = getint()
nums = getint()
for n in nums:
    # print n, last
    if n <= last:
        temp = (last - n) / d + 1
        count += temp
        last = n + d*temp
    else:
        last = n
print count