Description一个合法的串定义为：长度在\([l,r]\)之间，且只含0,1，并且不存在连续\(2\)个或更多的\(0\)。现在要选出\(k\)个长度相同的合法的串，问有几种选法，答案模\(10^9+7\)。\(1\leqk\leq200,1\leql\leqr\leq10^{18}\)。Solution容易发现答案为\(\sum_{i=l+2}^{r

考虑欧拉反演\[\sum\limits_{d\midn}\varphi(d)=n\]则原式可以化为\[\begin{align*}&\sum\limits_{i=1}^n\sum\limits_{j=1}^n\gcd(a_i,a_j)\cdot\gcd(i,j)\\=&\sum\limits_{i=1}^n\sum\limits_{j=1}^n\gcd(a_i,a_j)\sum\li

Theleavesrustlewhenthewindblows.Walkingonthesideoftheroadinaforeignland,IsighedthatitwasanotheryearoftheDragonBoatFestival.Asweallknow,DragonBoatFestivalisatraditionalchinesefestivaltoshowourrespecttoQuYuan.

DragonBoatFestivalHaveyoueverwonderedaboutafestivalthatintegratesthrillingboatraces,delicioustreats,andarichhistory?LooknofurtherthantheDragonBoatFestival!TheDragonBoatFestival,whichfallsonthefifthdayofthefifthlun

DragonBoatFestivalcandatebacktotheHandynasty，whichhasalonghistory.TheoriginsofDragonBoatFestivalhavebeenvariouslyexplainedsinceancienttimes.Thefestivalhasbeenendowedwithmanyculturalconnotationsinitsinheritancean

Asthesuncastitsgoldenraysoverthebustlingmarket,theairwasfilledwiththericharomaofbambooleavesandsteamingglutinousrice,whichsignaledthearrivaloftheDragonBoatFestival.Thescentofzongzi,wrappedtightlywiththesoundsof

TheDragonBoatFestival,celebratedonthefifthdayofthefifthlunarmonth,isatimeofgreatjoyandexcitementinChina.Itisafestivalrichinhistoryandtradition,honoringthememoryoftheancientpoetQuYuan.Lastdragonboatfestivalfor

DragonBoatFestivalTheDragonBoatFestival,atraditionalholidayinChina,fallsonthefifthdayofthefifthlunarmonth,anditsfestivitiesarefilledwithcolor,excitement,anddeepculturalsignificance.Andinmycommunity,weattachgreatimport

ShortTripIwenttoJiujianginJiangxiProvincewithmyroommate.Wedepart!Afteranhouronthemetro,weboardedthetrainasthebeginningofourpleasanttravel.Beautifulsceneryleapedtotheeyesthroughthetrainwindow,whichisoneoftherea

Listen,isthefootstepsoftheDragonBoatFestivalapproaching?DoyouknowDragonBoatFestival?WhenIwasalittlechild,IlearntknowledgeaboutDragonBoatFestival.TheDragonBoatFestivalalsoknownasDuanwuFestival,isatraditionalChinese

Asweallknow,theDragonBoatFestivalholdsprofoundhistoricalandculturalsignificance.TheDragonBoatFestivalwasoriginallyasummerfestivaltogetridofplague,andlateritwasusedasafestivalinmemoryofQuYuan.Dragonboatracingsymb

Thefestival,acommemorationoftheesteemedancientChinesepoetQuYuan,traditionallymarksatimeforfamilialreunions,thethrillingdragonboatraces,andtheindulgenceintraditionaldelicaciessuchaszongzi.However,thisyear,duetomystudi

TheDragonBoatFestivalThe Dragon Boat Festival, a time-honored traditional Chinese festival, merrily arrives on the fifth day of the fifth lunar month. It is said that this festival originated from the story of Qu Yuan. Qu 

InChina,theDragonBoatFestivaliscelebratedonday5ofthefifthmontheveryyearaccordingtotheChineselunarcalendar.EveryyearontheDragonBoatFestivalday,wegetupearlyandgetdowntomakezongzi.Weaddmeatorredbeansintoitdepe

FeedbackonnarrativewritingAfterpreliminarywritinganddesign,aswellastryingtocreatethefirstversionofthevideo,Ihaveidentifiedspecificshortcomingsinboththeprocessandresults,asfollowingbelow:Timetoolong.Accordingtothe

FestivalPreparationDuringtheDragonBoatFestival,ourfamily'spreparationsalwaysexudeastrongsenseofritual.Wehangwormwoodandcalamusathome,intendingtodriveawayevilspiritsandprayforthewell-beingofourfamily.Thistraditio

DragonBoatFestivalWiththeapproachingoftheDragonBoatFestival,thedesireofgoingbackhomebecamestrongerandstronger.AssoonasIarrivedhome,Ifeltrelaxedbecausethesmellofstickyriceandreedleavesfilledwiththeair.Itisfantast

​Intoday'svideo,IwanttointroducetheDragonBoatFestivaltoyou.TherearemanydifferentversionsregardingtheoriginofDragonBoatFestival,butthemostwidelyacceptedoneiscommemoratingthedeathofthepatrioticpoetQuYuan,whocom

TheDragonBoatFestival,atraditionalfestivaldeprivedfromChina,oftencelebratesonMay5andhaveolonghistory.BeforetheSpringandAutumnPeriodandtheWarringStatesPeriod,peopleheldDragonBoatFestivaltoeliminateillnessandmisfortun

Asthedrumbeatsechoacrossthewater,theairfillswiththefragrantscentofstickyriceandbamboo.It'stheDragonBoatFestival,avibrantcelebrationthatmarksthememoryofQuYuanandinvitesustoimmerseourselvesintherichtraditions

TheDragonBoatFestivalisaspecialholidayinChina.Ithappensonthefifthdayofthefifthmonthinthelunarcalendar.It'satimetorememberanoldpoetnamedQuYuanwholovedhiscountryverymuch.Today,wecelebratetheDragonBoatFesti

DragonBoatFestivalTheDragonBoatFestival,alsocalledtheDuanwuFestival,iscelebratedonthefifthdayofthefifthmonthaccordingtotheChinesecalendar.Forthousandsofyears,thefestivalhasbeenmarkedbyeatingzongziandracingdragon

TheDragonBoatFestival,atime-honoredtraditioninChina,encapsulatestheessenceofculture,family,andperseverance.ThisdayisalwaysfilledwithmarvelousdelightforaslongasIcanremember.Lastyear'sDragonBoatFestivalseemedlikey

TheEnchantmentoftheDragonBoatFestivalAstheearlyJuneiscoming,theringoftheDragonBoatFestivalhadunconsciouslyknocked.IwastransportedbacktotheenchantingatmosphereoftheDragonBoatFestival.Thisfestival,deeplyrootedinChin

TheDragonBoatFestivalapproaching,abuzzofanticipationfillstheair.Thisancientcelebration,passeddownfromgenerationtogeneration,notonlyrepresentsatimeforcommunity,butalsoajourneyofremembrance.Actually,Ididn'tpayattent