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())
s=input()
arr=[]
cnt=0
for i in range(n):
    arr.append(int(s.split(' ')[i]))
i=1
j=0
while i!=n:
    if arr[j]<arr[i]:
        i+=1
        j+=1
    elif arr[j]==arr[i]:
        cnt+=1
        arr[i]+=d
        i+=1
        j+=1
    elif arr[j]>arr[i]:
        k=arr[j]-arr[i]
        if k<d:
            if 2*k==d:
                cnt+=2
                arr[i]+=2*d
            else:
                cnt+=1
                arr[i]+=d
        else:
            if k%d>0:
                k=(k//d)+1
                cnt+=k
                arr[i]+=d*k
            else:
                k=(k//d)+1
                cnt+=k
                arr[i]+=d*k
        i+=1
        j+=1
print(cnt)