import java.util.Stack;

class Ackermann
{	
      public static long ack_rek(long n,long m)
      {
	 if (n==0) return m+1;
	 else if (m==0) return ack_rek(n-1,1);
	 else return ack_rek(n-1,ack_rek(n,m-1));
      }
      
      /*
       * @(#)Ackermann.java 1.0
       * Klaus Volbert, Oktober 2003
       */
      static final byte beginn=0;
      static final byte mitte=1;
      static final byte ende=2;
      
      public static long ack_it_KV(long n,long m)
      {
	 longStack st=new longStack();
	 st.push(ende);
	 st.push(n);
	 st.push(m);		
	 st.push(beginn);
	 byte pos;
       schleife:
	 while (true)
	  {
	     pos=(byte)st.pop();
	     switch (pos)
	      {
		 case beginn:
		 {
		    m=st.pop();
		    n=st.pop();
		    if (n==0) 
		     {
			long next=st.pop();
			st.push(m+1);
			st.push(next);
			continue schleife;
		     }
		    if (m==0)
		     {
			st.push(n-1);
			st.push(1);
			st.push(beginn);
			continue schleife;
		     }
		    st.push(n);
		    st.push(m);
		    st.push(mitte);
		    st.push(n);
		    st.push(m-1);
		    st.push(beginn);
		    continue schleife;
		 }
		 case mitte:
		 {
		    long zwi=st.pop();
		    m=st.pop();
		    n=st.pop();
		    st.push(n-1);
		    st.push(zwi);
		    st.push(beginn);
		    continue schleife;
		 }
		 case ende:
		 {
		    return st.pop();
		 }
	      }
	     return 0;
	  }
      }

      /**
       * @author Norbert Sondag
       */
      public static long ack_it_NS(long n,long m){
	 longStack stack = new longStack();
	 do{
	    if (n==-1)
	       n=stack.pop();
	    if (n==0){
	       m=m+1;
	       n=-1;
	    }
	    else if (m==0){
	       n--;
	       m=1;
	    }
	    else{
	       stack.push(n-1);
	       m--;
	    }
	 } while(n!=-1|!stack.empty());
	 return m;
      }

      /**
       * @author Mathias Raacke
       */
      public static long ack_it_MR(long n, long m)
      {
	 Stack nstack = new Stack();
	 nstack.push(new Long(n));
		
	 while (!nstack.empty())
	  {
	     n = ((Long)nstack.pop()).intValue();
	     while (n > 0)
	      {
		 if (m == 0)
		  {
		     n--;
		     m = 1;
		  }
		 else
		  {				
		     nstack.push(new Long(n-1));
		     m--;
		  }
	      }			
	     m++;
	  }
	 return m;
      }

      public static void main(String args[])
      {
	 for (long i=0;i<4;i++)
	  {
	     for (long j=0;j<10;j++)
	      {
		 System.out.print("ack("+i+","+j+"): "+ack_rek(i,j)+" (rek), ");
		 System.out.print(""+ack_it_KV(i,j)+" (it_KV), ");
		 System.out.print(""+ack_it_NS(i,j)+" (it_NS), ");
		 System.out.print(""+ack_it_MR(i,j)+" (it_MR)");
		 System.out.println();
	      }
	  }
	 System.out.println("ack(4,1)");
	 System.out.println(ack_it_KV(4,1));
      }
}

class longStack
{
      Stack stack;
      longStack() {
	 stack=new Stack();
      }
      public boolean empty()
      {
	 return stack.empty();
      }
      public void push(long l)
      {
	 stack.push(new Long(l));
      }
      public long pop()
      {
	 try
	  {
	     return ((Long)stack.pop()).longValue();
	  } catch (Exception e) {}
	 return -1;
      }
}