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 = input().split()
n,d = int(n[0]),int(n[1])
b = input()
b = [int(x) for x in b.split()]

res = 0
for i in range(n):
	if i == 0: continue
	if b[i] <= b[i-1]:
		res += (b[i-1] + 1 - b[i]) // d
		b[i] += (b[i-1] + 1 - b[i]) // d * d
		while b[i] <= b[i-1]:
			b[i] += d
			res += 1
	# print(res)
# print(b)
print(res)