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 ceil(a):
    if a.is_integer():
        return int (a)
    else:
        return int(a+1)
resp=0
a=raw_input().split()
for i in range(0,2):
    a[i]=int(a[i])
b=raw_input().split()
b[0]=int(b[0])
for i in range (1,a[0]):
    b[i]=int(b[i])
    while b[i-1]>=b[i]:
        if b[i]==b[i-1]:
            b[i]+=a[1]
            resp+=1
        else:
            c=ceil(float((b[i-1]-b[i]))/a[1])
            b[i]+=(c*a[1])
            resp+=c
print resp