#include<bits/stdc++.h> #define up(i,l,r) for(int i=(l);i<=(r);++i) #define down(i,l,r) for(int i=(l);i>=(r);--i) #define pi pair<int,int> #define p1 first #define p2 second #define m_p make_pair #define p_b push_back typedef long long ll; using namespace std; const int maxn=1e6+10,mod=998244353; inline ll read(){ ll x=0;short t=1;char ch=getchar(); while(ch<'0'||ch>'9'){if(ch=='-')t=-1;ch=getchar();} while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar(); return x*t; } int qp(int a,int b){ int res=1; while(b){ if(b&1)res=res*1ll*a%mod; a=a*1ll*a%mod;b>>=1; }return res; } const int G=3,Gi=(mod+1)/3; #define poly vector<int> int rev[1<<21],n; int trans(int x){ int res=0; down(i,n-1,0)res=(res<<1)+(x&1),x>>=1; return res; } int pw[1<<21]; int jc[maxn]; void NTT(poly &a,int op=1){ up(i,0,(1<<n)-1)rev[i]=trans(i); up(i,0,(1<<n)-1)if(i<rev[i])swap(a[i],a[rev[i]]); int x=op?G:Gi; int N=(1<<n); for(int k=1;k<N;k<<=1){ int v=qp(x,(mod-1)/k/2); pw[0]=1;up(i,1,k-1)pw[i]=pw[i-1]*1ll*v%mod; up(i,0,N-1)if(!(i&k)){ int p=pw[i&(k-1)]; int x=a[i],y=a[i+k]*1ll*p%mod; a[i+k]=(x-y+mod)%mod; a[i]=(x+y)%mod; } } if(!op){ int iv=qp(N,mod-2); for(int &x:a)x=x*1ll*iv%mod; } } poly operator*(poly a,poly b){ n=0;while((1<<n)<=(int)a.size()+(int)b.size()+5)n++; a.resize(1<<n),b.resize(1<<n); NTT(a,1);NTT(b,1); up(i,0,(1<<n)-1)a[i]=a[i]*1ll*b[i]%mod; NTT(a,0); while(a.size()&&(!a.back()))a.pop_back(); return a; } poly S; void get(int n){ jc[0]=1;up(i,1,n)jc[i]=jc[i-1]*1ll*i%mod; poly A(n+1),B(n+1); up(i,0,n)A[i]=qp(jc[i],mod-2)*1ll*((i&1)?(mod-1):1)%mod,B[i]=qp(i,n)*1ll*qp(jc[i],mod-2)%mod; S=A*B;S.resize(n+1); up(i,0,n)S[i]=S[i]*1ll*jc[i]%mod; } void solve_35pts(int n,int m,int x){ int M=1,res=0; up(i,1,x){ (res+=qp(x+1-i,n)*1ll*M%mod)%=mod; M=M*1ll*(m+i-1)%mod*1ll*qp(i,mod-2)%mod; } cout<<res; } const int T[]={1,373341033,45596018,834980587,623627864,428937595,442819817,499710224,833655840,83857087,295201906,788488293,671639287,849315549,597398273,813259672,732727656,244038325,122642896,310517972,160030060,483239722,683879839,712910418,384710263,433880730,844360005,513089677,101492974,959253371,957629942,678615452,34035221,56734233,524027922,31729117,102311167,330331487,8332991,832392662,545208507,594075875,318497156,859275605,300738984,767818091,864118508,878131539,316588744,812496962,213689172,584871249,980836133,54096741,417876813,363266670,335481797,730839588,393495668,435793297,760025067,811438469,720976283,650770098,586537547,117371703,566486504,749562308,708205284,932912293,939830261,983699513,206579820,301188781,593164676,770845925,247687458,41047791,266419267,937835947,506268060,6177705,936268003,166873118,443834893,328979964,470135404,954410105,117565665,832761782,39806322,478922755,394880724,821825588,468705875,512554988,232240472,876497899,356048018,895187265,808258749,575505950,68190615,939065335,552199946,694814243,385460530,529769387,640377761,916128300,440133909,362216114,826373774,502324157,457648395,385510728,904737188,78988746,454565719,623828097,686156489,713476044,63602402,570334625,681055904,222059821,477211096,343363294,833792655,461853093,741797144,74731896,930484262,268372735,941222802,677432735,474842829,700451655,400176109,697644778,390377694,790010794,360642718,505712943,946647976,339045014,715797300,251680896,70091750,40517433,12629586,850635539,110877109,571935891,695965747,634938288,69072133,155093216,749696762,963086402,544711799,724471925,334646013,574791029,722417626,377929821,743946412,988034679,405207112,18063742,104121967,638607426,607304611,751377777,35834555,313632531,18058363,656121134,40763559,562910912,495867250,48767038,210864657,659137294,715390025,865854329,324322857,388911184,286059202,636456178,421290700,832276048,726437551,526417714,252522639,386147469,674313019,274769381,226519400,272047186,117153405,712896591,486826649,119444874,338909703,18536028,41814114,245606459,140617938,250512392,57084755,157807456,261113192,40258068,194807105,325341339,884328111,896332013,880836012,737358206,202713771,785454372,399586250,485457499,640827004,546969497,749602473,159788463,159111724,218592929,675932866,314795475,811539323,246883213,696818315,759880589,4302336,353070689,477909706,559289160,79781699,878094972,840903973,367416824,973366814,848259019,462421750,667227759,897917455,81800722,956276337,942686845,420541799,417005912,272641764,941778993,217214373,192220616,267901132,50530621,652678397,354880856,164289049,781023184,105376215,315094878,607856504,733905911,457743498,992735713,35212756,231822660,276036750,734558079,424180850,433186147,308380947,18333316,12935086,351491725,655645460,535812389,521902115,67016984,48682076,64748124,489360447,361275315,786336279,805161272,468129309,645091350,887284732,913004502,358814684,281295633,328970139,395955130,164840186,820902807,761699708,246274415,592331769,913846362,866682684,600130702,903837674,529462989,90612675,526540127,533047427,110008879,674279751,801920753,645226926,676886948,752481486,474034007,457790341,166813684,287671032,188118664,244731384,404032157,269766986,423996017,182948540,356801634,737863144,652014069,206068022,504569410,919894484,593398649,963768176,882517476,702523597,949028249,128957299,171997372,50865043,20937461,690959202,581356488,369182214,993580422,193500140,540665426,365786018,743731625,144980423,979536721,773259009,617053935,247670131,843705280,30419459,985463402,261585206,237885042,111276893,488166208,137660292,720784236,244467770,26368504,792857103,666885724,670313309,905683034,259415897,512017253,826265493,111960112,633652060,918048438,516432938,386972415,996212724,610073831,444094191,72480267,665038087,11584804,301029012,723617861,113763819,778259899,937766095,535448641,593907889,783573565,673298635,599533244,655712590,173350007,868198597,169013813,585161712,697502214,573994984,285943986,675831407,3134056,965907646,401920943,665949756,236277883,612745912,813282113,892454686,901222267,624900982,927122298,686321335,84924870,927606072,506664166,353631992,165913238,566073550,816674343,864877926,171259407,908752311,874007723,803597299,613676466,880336545,282280109,128761001,58852065,474075900,434816091,364856903,149123648,388854780,314693916,423183826,419733481,888483202,238933227,336564048,757103493,100189123,855479832,51370348,403061033,496971759,831753030,251718753,272779384,683379259,488844621,881783783,659478190,445719559,740782647,546525906,985524427,548033568,333772553,331916427,752533273,730387628,93829695,655989476,930661318,334885743,466041862,428105027,888238707,232218076,769865249,730641039,616996159,231721356,326973501,426068899,722403656,742756734,663270261,364187931,350431704,671823672,633125919,226166717,386814657,237594135,451479365,546182474,119366536,465211069,605313606,728508871,249619035,663053607,900453742,48293872,229958401,62402409,69570431,71921532,960467929,537087913,514588945,513856225,415497414,286592050,645469437,102052166,163298189,873938719,617583886,986843080,962390239,580971332,665147020,88900164,89866970,826426395,616059995,443012312,659160562,229855967,687413213,59809521,398599610,325666688,154765991,159186619,210830877,386454418,84493735,974220646,820097297,2191828,481459931,729073424,551556379,926316039,151357011,808637654,218058015,786112034,850407126,84202800,94214098,30019651,121701603,176055335,865461951,553631971,286620803,984061713,888573766,302767023,977070668,110954576,83922475,51568171,60949367,19533020,510592752,615419476,341370469,912573425,286207526,206707897,384156962,414163604,193301813,749570167,366933789,11470970,600191572,391667731,328736286,30645366,215162519,604947226,236199953,718439098,411423177,803407599,632441623,766760224,263006576,757681534,61082578,681666415,947466395,12206799,659767098,933746852,978860867,59215985,161179205,439197472,259779111,511621808,145770512,882749888,943124465,872053396,631078482,166861622,743415395,772287179,602427948,924112080,385643091,794973480,883782693,869723371,805963889,313106351,262132854,400034567,488248149,265769800,791715397,408753255,468381897,415812467,172922144,64404368,281500398,512318142,288791777,955559118,242484726,536413695,205340854,707803527,576699812,218525078,875554190,46283078,833841915,763148293,807722138,788080170,556901372,150896699,253151120,97856807,918256774,771557187,582547026,472709375,911615063,743371401,641382840,446540967,184639537,157247760,775930891,939702814,499082462,19536133,548753627,593243221,563850263,185475971,687419227,396799323,657976136,864535682,433009242,860830935,33107339,517661450,467651311,812398757,202133852,431839017,709549400,99643620,773282878,290471030,61134552,129206504,929147251,837008968,422332597,353775281,469563025,62265336,835064501,851685235,21197005,264793769,326416680,118842991,84257200,763248924,687559609,150907932,401832452,242726978,766752066,959173604,390269102,992293822,744816299,476631694,177284763,702429415,374065901,169855231,629007616,719169602,564737074,475119050,714502830,40993711,820235888,749063595,239329111,612759169,18591377,419142436,442202439,941600951,158013406,637073231,471564060,447222237,701248503,599797734,577221870,69656699,51052704,6544303,10958310,554955500,943192237,192526269,897983911,961628039,240232720,627280533,710239542,70255649,261743865,228474833,776408079,304180483,63607040,953297493,758058902,395529997,156010331,825833840,539880795,234683685,52626619,751843490,116909119,62806842,574857555,353417551,40061330,822203768,681051568,490913702,9322961,766631257,124794668,37844313,163524507,729108319,490867505,47035168,682765157,53842115,817965276,757179922,339238384,909741023,150530547,158444563,140949492,993302799,551621442,137578883,475122706,443869843,605400098,689361523,769596520,801661499,474900284,586624857,349960501,134084537,650564083,877097974,379857427,887890124}; int JC(int x){ int B=1e6; int res=T[x/B]; up(i,x/B*B+1,x)res=res*1ll*i%mod; return res; } void solve_55pts(int n,int m,int x){ get(n); //int res=1;up(i,x+1,x+m)res=res*1ll*i%mod; //up(i,1,m)res=res*1ll*qp(i,mod-2)%mod; int res=JC(x+m)*1ll*qp(JC(x),mod-2)%mod*1ll*qp(JC(m),mod-2)%mod; int ans=0; up(i,0,n){ //cout<<res<<" "<<S[i]<<endl; (ans+=res*1ll*S[i]%mod)%=mod; res=res*1ll*qp(i+1+m,mod-2)%mod*1ll*(x-i)%mod; }cout<<ans; } const int MAXN=2e7+10; #define jc jcc int w[MAXN],p[MAXN],s[MAXN],iv[MAXN]; int jc[MAXN],jc_inv[MAXN]; int get_C(int n,int m){if(n<0||m<0||m<n)return 0;return JC(m)*1ll*qp(JC(n),mod-2)%mod*1ll*qp(JC(m-n),mod-2)%mod;} void solve_15pts(int n,int m,int x){ int c=0;w[1]=1; up(i,2,2e7){ if(!w[i])w[i]=qp(i,n),p[++c]=i; up(j,1,c){ if(i*p[j]>2e7)break; w[i*p[j]]=w[i]*1ll*w[p[j]]%mod; if(!(i%p[j]))break; } } int need=min(n+m+5,x),M=JC(x-need+m-1)*1ll*qp(JC(m-1),mod-2)%mod*1ll*qp(JC(x-need),mod-2)%mod; down(i,need,1){ w[i]=w[i]*1ll*M%mod; M=M*1ll*(m+x-i)%mod*1ll*qp(x-i+1,mod-2)%mod; } jc[0]=1;up(i,1,need)jc[i]=jc[i-1]*1ll*i%mod; jc_inv[need]=qp(jc[need],mod-2);down(i,need,1)jc_inv[i-1]=jc_inv[i]*1ll*i%mod; jc[0]=1;up(i,1,need)jc[i]=jc[i-1]*1ll*(x-i)%mod; iv[need]=qp(jc[need],mod-2);down(i,need,1)iv[i-1]=iv[i]*1ll*(x-i)%mod; up(i,1,need)iv[i]=iv[i]*1ll*jc[i-1]%mod; up(i,1,need)(w[i]+=w[i-1])%=mod; if(x<=need){cout<<w[x];return;} int res=0,v=JC(x-1)*1ll*qp(JC(x-1-need),mod-2)%mod; up(i,1,need)(res+=w[i]*1ll*v%mod*1ll*jc_inv[i-1]%mod*1ll*jc_inv[need-i]%mod*1ll*iv[i]%mod*1ll*(((need-i)&1)?mod-1:1)%mod)%=mod; cout<<res; } #undef jc void slv(){ int n=read(),m=read(),x=read(); if(x<=1e7){ solve_35pts(n,m,x); return; } if(n<=1e6){ solve_55pts(n,m,x); return; } if(n+m<=2e7){ solve_15pts(n,m,x); return; } } int main(){ //freopen("old.in","r",stdin); //freopen("old.out","w",stdout); slv(); fclose(stdin); fclose(stdout); return 0; }