C Programming Challenge

Hey poseurs.  We got one for you.

Write a C program to compute the subfactorial of an integer N.

Y'all have heard of a factorial.  How 'bout a subfactorial?

Here is a sequence of subfactorials for N = {1 ... 23}:

https://oeis.org/A000166

Up to only 23???!!!

Sheesh!  We can do better than than:

[~] ./subfact 100

34332795984163804765195977526776142032365783805375784983543400282685180793327632432791396429850988990237345920155783984828001486412574060553756854137069878601

Want more?  Sure thing:

[~] ./subfact 1000

148030000371669080363916614118966054237787246771683461554691846089888817122236071181318987391054867545959072618913067395256592673937835956772241168222528295595683596720980666220609427831904885242029599391814586746492963217722340317777195575260366010059010655172144738284878861758208131004735035818477569368786432061632016188446807685910940321832572996649981481772252325191040086154426554657538458444535765717871033946613771702350305625265004320388243386097879262683082846870385959781954488956389970392578944288660459295031234507478736716881824136783622584535138805982288145285315709292044924680549217929790115984545014441521755735726306195457199770572691754663617787391418043564291295463544232345623814234091075245481655240617768194600801613370454579550360990469214942505585371933295794820730182459765487139302567668926438713305035074950095908181875721870629028442704188817930628082595769711646309710902713389577813924985084195489687602046619502008960961979336971200011845832972766496820425232309014424160383352549432587175804599513224295387620793237492133106194854781675335264245443368406349778626577154153936165795176414280246708209684255021094823421966794931258601926237888502063061179908920389122437280096694180318756729540187743522955287693403344627192008193243150047926683116206789808737520329932175926689631039801333205271773068694119886681439408208634536616162125484968246433299086618972038726320143524530159155122816067209479359158975104676175689942972909538981915518610438058966813454552135810617643268326508884740007563057812557756872119827948177012498720002846584320083602883505675223930415710240943383142087697091237570482781352256162809593048997307636369071690373544475334727722226964401838105804104033698859046508072636221121284767256179261384695575800126777871914608799740333135169078085040301870738700721986026518324144597854534393940110548874771456733548819690014891150299883374569036144504075650284247154291122602262577738634502394468066637260601515590412677997656372138988479892629787344855469625993188902215341743976591335786134612426484416557074485085137922648888557127618980204107341206517456111787177656668620397156874752365541689736459115633909848251703534756902949331850082296669410306980175719986482188446333446450823956158029544268395051423740042819986368612454904255206373684842598857136228239326853906860111911390847498545181350875035398066868621959973870036473108206470890805125591766035651660263166256071859066523494404932873989243033885387310363168734739688132495065765084286985470381074859852651721482664917019227944750044815550686001

Now you try.

C only.

See y'all in 2632.

Ha, ha, ha, ha, ha, ha, ha, ha, ha, ha!