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 itertools import product

file = sys.stdin
#file = open("test", "r")

n, d = map(int, file.readline().rstrip().split())
p = map(int, file.readline().rstrip().split())
cnt = 0
for i in range(1, len(p)):
    if p[i] <= p[i - 1]:
        cnt += (p[i - 1] - p[i])/d + 1
        p[i] = p[i] + ((p[i - 1] - p[i])/d + 1)*d

print cnt
