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
nd = raw_input().split()
n = int(nd[0])
d = int(nd[1])

numList = raw_input().split()
for i in range(n):
    numList[i] = int(numList[i])

ans = 0
for i in range(n-1):
    difference = numList[i] - numList[i+1]
    if difference >= 0:
        iterations = 1 + (difference / d)
        numList[i+1] += d * iterations
        ans += iterations
print ans