$1=1        # $0,$1 := 0,1;
$3=N/K
while$1<=$3 # while $1 <= N/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