The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.



The Ackermann function is usually defined as follows:







A
(
m
,
n
)
=


{



n
+
1



if 

m
=
0




A
(
m
−
1
,
1
)



if 

m
>
0

 and 

n
=
0




A
(
m
−
1
,
A
(
m
,
n
−
1
)
)



if 

m
>
0

 and 

n
>
0.








{\displaystyle A(m,n)={\begin{cases}n+1&{\mbox{if }}m=0\\A(m-1,1)&{\mbox{if }}m>0{\mbox{ and }}n=0\\A(m-1,A(m,n-1))&{\mbox{if }}m>0{\mbox{ and }}n>0.\end{cases}}}






Its arguments are never negative and it always terminates.



Task

Write a function which returns the value of 



A
(
m
,
n
)


{\displaystyle A(m,n)}

. Arbitrary precision is preferred (since the function grows so quickly), but not required.



See also

 Conway chained arrow notation for the Ackermann function.


Private Function Ackermann_function(m As Variant, n As Variant) As Variant
    Dim result As Variant
    Debug.Assert m >= 0
    Debug.Assert n >= 0
    If m = 0 Then
        result = CDec(n + 1)
    Else
        If n = 0 Then
            result = Ackermann_function(m - 1, 1)
        Else
            result = Ackermann_function(m - 1, Ackermann_function(m, n - 1))
        End If
    End If
    Ackermann_function = CDec(result)
End Function
Public Sub main()
    Debug.Print "           n=",
    For j = 0 To 7
        Debug.Print j,
    Next j
    Debug.Print
    For i = 0 To 3
        Debug.Print "m=" & i,
        For j = 0 To 7
            Debug.Print Ackermann_function(i, j),
        Next j
        Debug.Print
    Next i
End Sub