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 = list(map(int,input().split()))
ss = []
for i in range(n-1):
    if s[i] >= s[i+1]:
        k = (s[i] - s[i+1]) // d
        ss.append((k+1)*d)
        s[i+1] = s[i+1]+(k+1)*d
    else:
        continue
        
          
print(int(sum(ss)/d))