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
#!/usr/bin/env python2
# -*- coding: utf-8 -*-
import sys
input = sys.stdin
output = sys.stdout

def solve(A,d):
    n = 0
    for i in range(1,len(A)):
        prev = A[i-1]
        a = A[i]
        if a > prev:
            continue
        dn = (prev-a) / d + 1
        A[i] += dn * d
        n += dn
    return n

def numbers_from_line(d=' '):
    return [int(s) for s in input.readline().strip().split(d) if len(s.strip())>0]

A = numbers_from_line()
n = A[0]
d = A[1]
A = numbers_from_line()

a = solve(A,d)
output.write('%s\n' % a)
