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.


import extensions;
 
ackermann(m,n)
{
    if(n < 0 || m < 0)
    {
        InvalidArgumentException.raise()
    };
 
    m =>
       0 { ^n + 1 }
       : {
              n => 
                0 { ^ackermann(m - 1,1) }
                : { ^ackermann(m - 1,ackermann(m,n-1)) }
           }
}
 
public program()
{
    for(int i:=0, i <= 3, i += 1)
    {
        for(int j := 0, j <= 5, j += 1)
        {
            console.printLine("A(",i,",",j,")=",ackermann(i,j))
        }
    };
 
    console.readChar()
}