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.


Program Ackerman;
 
function ackermann(m, n: Integer) : Integer;
begin
   if m = 0 then
      ackermann := n+1
   else if n = 0 then
      ackermann := ackermann(m-1, 1)
   else
      ackermann := ackermann(m-1, ackermann(m, n-1));
end;
 
var
   m, n	: Integer;
 
begin
   for n := 0 to 6 do
      for m := 0 to 3 do
	 WriteLn('A(', m, ',', n, ') = ', ackermann(m,n));
end.