Fix factorial symbol and change variable k to n

.latexmkrc

@@ -1,4 +1,3 @@
 $pdflatex="pdflatex -shell-escape -interaction=nonstopmode -synctex=1 %O %S";
 $out_dir = 'build';
 $pdf_mode = 1;
-

Makefile

@@ -1,19 +1,25 @@
 PRESENTATIONS := $(patsubst src/%/presentation.tex,build/presentation_%.pdf,$(wildcard src/*/presentation.tex))
 HANDOUTS := $(patsubst build/presentation_%.pdf,build/presentation_%_handout.pdf,$(PRESENTATIONS))
 
+RC_PDFLATEX := $(shell grep '$$pdflatex' .latexmkrc \
+	       | sed -e 's/.*"\(.*\)".*/\1/' -e 's/%S//' -e 's/%O//')
+
 .PHONY: all
 all: $(PRESENTATIONS) $(HANDOUTS)
 
 build/presentation_%.pdf: src/%/presentation.tex build/prepared
-	TEXINPUTS=./lib/cel-slides-template-2025:$$TEXINPUTS latexmk $<
+	TEXINPUTS=./lib/cel-slides-template-2025:$(dir $<):$$TEXINPUTS \
-	mv build/presentation.pdf $@
+		latexmk -outdir=build/$* $<
+	cp build/$*/presentation.pdf $@
 
 build/presentation_%_handout.pdf: src/%/presentation.tex build/prepared
-	TEXINPUTS=./lib/cel-slides-template-2025:$$TEXINPUTS latexmk -pdflatex='pdflatex %O "\def\ishandout{1}\input{%S}"' $<
+	TEXINPUTS=./lib/cel-slides-template-2025:$(dir $<):$$TEXINPUTS \
-	mv build/presentation.pdf $@
+		latexmk -outdir=build/$*_handout \
+		-pdflatex='$(RC_PDFLATEX) %O "\def\ishandout{1}\input{%S}"' $<
+	cp build/$*_handout/presentation.pdf $@
 
 build/prepared:
-	mkdir -p build
+	mkdir build
 	touch build/prepared
 
 .PHONY: clean