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 sys
from math import ceil
import logging
logging.root.setLevel(logging.INFO)

n,k = map(int,sys.stdin.readline().strip().split())
nums = list(map(int,sys.stdin.readline().strip().split()))
deltas = []
times = 0
for i in range(1,len(nums)):
    if nums[i-1] >= nums[i]:
        delta = ceil((nums[i-1]+1 - nums[i])/k)
        times += delta
        nums[i] += delta*k
    
print(times)
