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=list(map(int,input().split()))
x=list(map(int,input().split()))
count=0
diff=0
for i in range(1,n[0]):
  if x[i]<=x[i-1]:
    diff=x[i-1]-x[i]
    if diff<n[1]-1:
      count+=1
      x[i]+=n[1]
    else:
      new=diff//n[1]
      count+=(new+1)
      x[i]+=n[1]*(new+1)
      
# print(x)
print(count)