$0=K        # $0 := K = U_2(K,-1);
$1=K*K      # $1 := K**2+2 = V_2(K,-1);
$1=$1+2
$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
$2=K*$0     # $0,$1 := ($0),((K*$0)+$1)/2 = U_{n}(K,-1),U_{n+1}(K,-1); (where n mod 2 = 0)
$1=$1+$2
$1=$1/2
$3=1000000000/K
while$1<=$3 # while $1<=10**9/K:
  $2=$1*K   #   $1,$0 := ((($1*K+$0)*K+$1),($1*K+$0))
  $0=$2+$0
  $2=$0*K
  $1=$1+$2
end         # end
$0=$0*N     # return ($0*N/$1+N);
$0=$0/$1
$0=$0+N
return$0