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
import re
from fractions import Fraction

class Task:
    b = []
    d = 0
    answer = 0
    
    def __init__(self):
        n, self.d = [int(x) for x in input().split()]
        self.b = [int(x) for x in input().split()]

    def solve(self):
        b, d = self.b, self.d
        for i in range(1, len(b)):
            if b[i] <= b[i - 1]:
                numberOfSteps = (b[i - 1] - b[i]) // d + 1
                b[i] += numberOfSteps * d
                self.answer += numberOfSteps

    def printAnswer(self):
        print(self.answer)

task = Task()
task.solve()
task.printAnswer()
