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
import math
n, d = [int(x) for x in input().split()]
b = [int(x) for x in input().split()]

moves = 0
bench = 0

for i in range(1, len(b)):
    if b[i] < b[i - 1]:
        bench = math.ceil((b[i - 1] - b[i]) / d)
        b[i] += (d * bench)
        moves += bench
    if b[i] == b[i - 1]:
        b[i] += d
        moves += 1
   
print(moves)
