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 = list(map(int, input().split(' '))) #input numbers n and d
numbers = list(map(int, input().split(' '))) #imput series
count = 0 #initialize counter

for i in range(1,n):
    if numbers[i] <= numbers[i-1]: #if previous number is is equal or greater than the next one, we increase the second with d while it is still smaller or equal
        mult = (numbers[i - 1] - numbers[i]) // d + 1
        numbers[i] += mult * d
        count += mult

print(count) #print answer