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
#!/usr/bin/python

import math

n, d = raw_input().split()
n = int(n)
d = int(d)
b = raw_input().split()

for i in xrange(len(b)):
	b[i] = int(b[i])

ans = 0
for i in xrange(1, len(b)):
	if(b[i] < b[i - 1]):
		cnt = int(math.ceil((b[i - 1] - b[i]) * 1. / d));
		b[i] += d * cnt
		ans += cnt

	if(b[i] == b[i - 1]):
		b[i] += d
		ans += 1

print ans
		
