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 = map(int, input().split())
lista = input().split()
count = 0

for i in range(n-1):
    w = int(lista[i+1]) - int(lista[i])
    if w < 0 and w%d !=0:
        c = math.ceil(-w / d)
        lista[i+1] = int(lista[i+1]) + d*c
        count += c
       
    elif w < 0 and w%d ==0:
        c = math.ceil(-w / d)
        lista[i+1] = int(lista[i+1]) + d*(c+1)
        count += c+1
        
    elif w == 0:
        lista[i+1] = int(lista[i+1]) + d
        count += 1
        
print (count)