ifK<=2      # if K<=2:
  $1=K*K    #   $0 := (K**2+1)*(K**3+3*K) = U_6(K,-1);
  $0=$1+1   #   $1 := (K**3+3*K)**2+2 = V_6(K,-1);
  $1=$1+3
  $1=$1*K
  $0=$0*$1
  $1=$1*$1
  $1=$1+2
end         # end
ifK>=3      # if K>=3:
  $0=K      #   $0 := K = U_2(K,-1);
  $1=K*K    #   $1 := K**2+2 = V_2(K,-1);
  $1=$1+2
end         # end
$3=100000/K
while$0<$3  # while $0<10**5/K:
  $0=$0*$1  #   $0,$1 := ($0*$1),($1*$1-2) = U_{2n}(K,-1),V_{2n}(K,-1); (where n mod 2 = 0)
  $1=$1*$1
  $1=$1-2
end         # end
$3=K*$0     # $1,$0,$2 := ($1+(K*$0))/2,$0,($1-(K*$0))/2 = U_{n+1}(K,-1),U_{n}(K,-1),U_{n-1}(K,-1); (where n mod 2 = 0)
$2=$1-$3
$2=$2/2
$1=$1+$3
$1=$1/2
$4=N/K
while$1<=$4 # while $1 <= (N/K):
  $2=$1     #   $1,$0,$2 := (($1*K+$0)*K+$1),($1*K+$0),($1);
  $3=$1*K
  $0=$3+$0
  $1=$0*K
  $1=$1+$2
end         # end
if$0<=$4    # if $0 <= (N/K):
  $2=$0     #   $1,$0,$2 := ($1*K+$0),($1),($0);
  $0=$1
  $1=$0*K
  $1=$1+$2
end         # end
if$0<=N     # if $0 <= N:
  $3=N/$0   #   $3 := N/$0+1;
  $3=$3+1
  $1=$1*$3  #   $1 := $1*$3+$0;
  $1=$1+$0
  $0=$0*$3  #   $0 := $0*$3+$2;
  $0=$0+$2
end         # end
$2=$1-$0    # $0,$2 := ($0*N),($1-$0);
$0=$0*N
ifM==0      # if M==0:
  $2=$2+K   #   $0 := $0-($2+K-1)/K;
  $2=$2-1
  $2=$2/K
  $0=$0-$2
end         # end
ifM>1       # if M>1:
  $3=M-1    #   $3 := M-1;
  $4=$2/K   #   $0 := $0+($2/K)*(M-1);
  $4=$4*$3
  $0=$0+$4
  $2=$2%K   #   $0 := $0+($2%K)*(M-1)/K;
  $2=$2*$3
  $2=$2/K
  $0=$0+$2
end         # end
$0=$0/$1    # return ($0/$1+N);
$0=$0+N
return$0