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,k = list(map(int, input().split(' ')))
nums = list(map(int, input().split(' ')))
result = 0
for i in range(1,n):
    if nums[i] == nums[i-1]:
        result += 1
        nums[i] += k
    elif nums[i] < nums[i-1]:
        nk = (nums[i-1] - nums[i]) // k + 1
        result += nk
        nums[i] += nk * k
print(result)