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


__author__ = 'Obriel Muga'

n,d = list(map(int,input().strip().split()))
secuencia = list(map(int,input().strip().split()))
resto = 0
contador_op = 0
for i in range(n-1):
    valor = ((secuencia[i+1] - secuencia[i]))
    if (valor - resto > 0):
        resto = 0
        continue
    elif (valor - resto == 0):
        contador_op += 1
        resto = d
    elif (valor - resto < 0):
        if (abs(valor - resto))%d == 0:
            agregar = math.ceil(abs(valor-resto)/d) + 1
        else:
            agregar = math.ceil(abs(valor - resto)/d)
        contador_op += agregar
        resto = agregar*d    
print(contador_op)
