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.


 
--#SET TERMINATOR @
 
SET SERVEROUTPUT ON@
 
CREATE OR REPLACE FUNCTION ACKERMANN(
  IN M SMALLINT,
  IN N BIGINT
 ) RETURNS BIGINT
 BEGIN
  DECLARE RET BIGINT;
  DECLARE STMT STATEMENT;
 
  IF (M = 0) THEN
   SET RET = N + 1;
  ELSEIF (N = 0) THEN
   PREPARE STMT FROM 'SET ? = ACKERMANN(? - 1, 1)';
   EXECUTE STMT INTO RET USING M;
  ELSE
   PREPARE STMT FROM 'SET ? = ACKERMANN(? - 1, ACKERMANN(?, ? - 1))';
   EXECUTE STMT INTO RET USING M, M, N;
  END IF;
  RETURN RET;
 END @
 
BEGIN
 DECLARE M SMALLINT DEFAULT 0;
 DECLARE N SMALLINT DEFAULT 0;
 DECLARE MAX_LEVELS CONDITION FOR SQLSTATE '54038';
 DECLARE CONTINUE HANDLER FOR MAX_LEVELS BEGIN END;
 
 WHILE (N <= 6) DO
  WHILE (M <= 3) DO
   CALL DBMS_OUTPUT.PUT_LINE('ACKERMANN(' || M || ', ' || N || ') = ' || ACKERMANN(M, N));
   SET M = M + 1;
  END WHILE;
  SET M = 0;
  SET N = N + 1;
 END WHILE;
END @
 