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())
arr = [int(i) for i in input().split()]
ans = 0
for i in range(1, n):
    if arr[i] <= arr[i - 1]:
        l, r = 0, 10 ** 8
        while (r - l) > 1:
            mid = (r + l) // 2
 
            k = mid * d
 
            if (arr[i] + k) > arr[i - 1]:
                r = mid
            else:
                l = mid
        
        arr[i] += r * d
        ans += r
 
print(ans)