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
x=input()
x=x.split()
arreglo=input()
arreglo=arreglo.split()
suma=0
contador=0
k=-1
for a in range (int(x[0])):
        if int(arreglo[1])==int(arreglo[a]):
                contador=contador+1
if contador==(int(x[0]))and int(x[0])>2:
        suma=(contador*(contador-1))//2
else:
        for p in range (1,len(arreglo)):
                k=k+1
                if int(arreglo[k])>=int(arreglo[p]):
                        u=int(arreglo[k])-int(arreglo[p])
                        s=(u//int(x[1]))+1
                        arreglo[p]=int(arreglo[p])+(int(x[1])*s)
                        suma=suma+s
                        
print(suma)