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
'''
Created on 6 Apr 2011

@author: salama
'''
n, k = map(int,raw_input().split())
ans = 0
b = map(int,raw_input().split())
for i in range(1,n):
    if b[i] <= b[i-1]:
        z = 0
        z += 1 if ((b[i-1] - b[i]) + 1) % k != 0 else 0
        z += ((b[i-1] - b[i]) + 1) / k
        b[i] += k*z
        ans += z
print ans