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
import math
n,m=[int(i) for i in input().split()]
a=[int(i) for i in input().split()]
s=0
for i   in range(1,len(a)):
    if(a[i]>a[i-1]):
        pass
    else:
        e=abs(a[i]-a[i-1])+1
        s=s+(math.ceil(e/m))
        a[i]=a[i]+(math.ceil(e/m)*m)
print(s)