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,d=(int(x) for x in input().split())
a=list(int(x) for x in input().split())
ans=0
for i in range(1,n):
    diff=a[i]-a[i-1]
    #print(f"a[i] is {a[i]} and a[i-1] is {a[i-1]} and diff is {diff}")
    if(diff<0):
        diff*=-1        
        num=math.ceil(diff/d)
        #print("adding ",num)
        ans+=num
        a[i]+=num*d
        diff-=num*d
    if diff==0:
        a[i]+=d
        ans+=1
    #print(a)
    #print("\n")

print(ans)

