human
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

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Give me a the least number of moves required to make the given sequence increasing?
assistant
#Here is the least number of moves required to make the given sequence increasing.

import sys
from math import sqrt, floor, factorial, gcd
from collections import deque, Counter
inp = sys.stdin.readline
read = lambda: list(map(int, inp().strip().split()))

def solve():
	n, d = read()
	arr = read(); curr = arr[0]
	count = 0
	for i in range(1, n):
		# print(curr, arr[i], i, count)
		if curr >= arr[i]:
			diff = curr-arr[i]
			arr[i] += d*(diff//d)
			count += (diff//d)
			if curr >= arr[i]:
				arr[i] += d
				count += 1
		curr = arr[i]
	print(count)



# def solve():
# 	ans = ""
# 	for _ in range(int(inp())):
# 		n, c = read(); arr = []
# 		for i in range(n): arr.append(int(inp()))
# 		arr.sort()
# 		max_ans = 1
# 		low = arr[0]; high = arr[-1]
# 		while low < high:
# 			mid = (low+high)//2
# 			# print(low, high, mid, "**")
# 			count = 1; left = arr[0]
# 			for i in range(1, n):
# 				right = arr[i]
# 				if right-left >= mid:
# 					# print(right-left, mid)
# 					count += 1
# 					left = right
# 			# print(count)
# 			if count >= c:
# 				low = mid+1
# 				max_ans = max(max_ans, mid)
# 			else:
# 				high = mid-1
			
# 		ans += str(max_ans)+"\n"
# 	return(ans)



if __name__ == "__main__":
	solve()
	# print(solve())