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
def mp():  return map(int,input().split())
def lt():  return list(map(int,input().split()))
def pt(x):  print(x)
def ip():  return input()
def it():  return int(input())
def sl(x):  return [t for t in x]
def spl(x): return x.split()
def aj(liste, item): liste.append(item)
def bin(x):  return "{0:b}".format(x)
def listring(l): return ' '.join([str(x) for x in l])
def printlist(l): print(' '.join([str(x) for x in l]))
    
n,d = mp()
a = lt()
b = 0
c = 0
for i in range(1,len(a)):
    if a[i] <= a[i-1]+d*b:
        b = (a[i-1]+d*b-a[i])//d + 1
        c += b
    else:
        b = 0
print(c)
        
        
        
    