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,d=input().split()
n=int(n)
d=int(d)
#print(n,d)
a=[]
inp=input().split()
for i in range(0,len(inp)):
    a.append(int(inp[i]))   
cnt=0
import math
for i in range (0,n-1):
    if a[i]>=a[i+1]:
        vag=math.floor((a[i]-a[i+1])/d)
        cnt=cnt+vag+1
        a[i+1]=a[i+1]+((vag+1)*d)
print(cnt)
        
