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.


for m = 0 to 3
        for n = 0 to 4
                see "Ackermann(" + m + ", " + n + ") = " + Ackermann(m, n) + nl
         next
next
 
func Ackermann m, n
        if m > 0
           if n > 0
                return Ackermann(m - 1, Ackermann(m, n - 1))
            but n = 0
                return Ackermann(m - 1, 1)
            ok 
        but m = 0
            if n >= 0 
                return n + 1
            ok
        ok
Raise("Incorrect Numerical input !!!") 