$1=1        # $0,$1 := 0,1;
while$1<=N  # while $1 <= N:
  $2=$1*K   #   $0,$1 := $1,($1*K+$0);
  $2=$2+$0
  $0=$1
  $1=$2
end         # end
$0=$0*N     # return ($0*N/$1+N);
$0=$0/$1
$0=$0+N
return$0