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.


HAI 1.3
 
HOW IZ I ackermann YR m AN YR n
    NOT m, O RLY?
        YA RLY, FOUND YR SUM OF n AN 1
    OIC
 
    NOT n, O RLY?
        YA RLY, FOUND YR I IZ ackermann YR DIFF OF m AN 1 AN YR 1 MKAY
    OIC
 
    FOUND YR I IZ ackermann YR DIFF OF m AN 1 AN YR...
     I IZ ackermann YR m AN YR DIFF OF n AN 1 MKAY MKAY
IF U SAY SO
 
IM IN YR outer UPPIN YR m TIL BOTH SAEM m AN 5
    IM IN YR inner UPPIN YR n TIL BOTH SAEM n AN DIFF OF 6 AN m
        VISIBLE "A(" m ", " n ") = " I IZ ackermann YR m AN YR n MKAY
    IM OUTTA YR inner
IM OUTTA YR outer
 
KTHXBYE