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=map(int, input().split())
a=list(map(int, input().split()))
k=0
p=0
for i in range(1,N):
    if (a[i]<a[i-1]):
        if (a[i-1]-a[i])%D==0:
            p=(a[i-1]-a[i])//D
            k+=p
        else:
            p=(a[i-1]-a[i])//D+1
            k+=p
        a[i]+=p*D
    if (a[i]==a[i-1]):
        p=1
        k+=1
        a[i]+=p*D
print(k)