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()

d = int(d)

def inp(s):
    j = 0
    a = []
    for i in range(len(s)):
        if s[i] == " ":
            a.append(int(s[j:i]))
            j = i+1
        if i == len(s)-1:
            a.append(int(s[j:]))
    return a

s = input()
a = inp(s)
c = 0
for i in range(len(a)-1):
    if a[i+1] > a[i]:
        continue
    else:
        t = a[i] - a[i+1]
        
        if t<d:
            a[i+1] = a[i+1] + d
            c = c + 1
        else:
            t = t//d + 1
            c = c + t
            a[i+1] = a[i+1] + t*d
print (c)
