結果

問題 No.2747 Permutation Adjacent Sum
ユーザー otoshigootoshigo
提出日時 2024-04-20 13:27:04
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 342 ms / 3,000 ms
コード長 11,952 bytes
コンパイル時間 2,484 ms
コンパイル使用メモリ 201,836 KB
実行使用メモリ 104,896 KB
最終ジャッジ日時 2024-04-20 13:27:15
合計ジャッジ時間 9,745 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 120 ms
41,384 KB
testcase_01 AC 14 ms
6,144 KB
testcase_02 AC 74 ms
27,520 KB
testcase_03 AC 15 ms
6,520 KB
testcase_04 AC 122 ms
44,652 KB
testcase_05 AC 319 ms
104,356 KB
testcase_06 AC 133 ms
48,572 KB
testcase_07 AC 108 ms
39,664 KB
testcase_08 AC 184 ms
65,348 KB
testcase_09 AC 291 ms
90,952 KB
testcase_10 AC 30 ms
13,692 KB
testcase_11 AC 113 ms
40,240 KB
testcase_12 AC 5 ms
5,376 KB
testcase_13 AC 50 ms
19,704 KB
testcase_14 AC 162 ms
58,896 KB
testcase_15 AC 263 ms
88,712 KB
testcase_16 AC 121 ms
42,620 KB
testcase_17 AC 247 ms
82,204 KB
testcase_18 AC 233 ms
78,408 KB
testcase_19 AC 20 ms
9,708 KB
testcase_20 AC 119 ms
44,428 KB
testcase_21 AC 188 ms
66,048 KB
testcase_22 AC 208 ms
71,040 KB
testcase_23 AC 96 ms
34,396 KB
testcase_24 AC 100 ms
36,840 KB
testcase_25 AC 67 ms
25,208 KB
testcase_26 AC 165 ms
60,172 KB
testcase_27 AC 207 ms
68,000 KB
testcase_28 AC 186 ms
64,328 KB
testcase_29 AC 125 ms
45,036 KB
testcase_30 AC 322 ms
104,896 KB
testcase_31 AC 317 ms
104,788 KB
testcase_32 AC 342 ms
104,800 KB
testcase_33 AC 335 ms
104,896 KB
testcase_34 AC 326 ms
104,876 KB
testcase_35 AC 2 ms
5,376 KB
testcase_36 AC 2 ms
5,376 KB
testcase_37 AC 2 ms
5,376 KB
testcase_38 AC 2 ms
5,376 KB
testcase_39 AC 2 ms
5,376 KB
testcase_40 AC 1 ms
5,376 KB
testcase_41 AC 1 ms
5,376 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<bits/stdc++.h>
using namespace std;
using ll=long long;
#define rep(i,n) for(int i=0;i<n;i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
template<class T> bool chmax(T &a, T b){if (a < b){a = b;return true;} else return false;}
template<class T> bool chmin(T &a, T b){if (a > b){a = b;return true;} else return false;}

const int MOD=998244353;

template<class T>
struct lagrange_interpolation{
    int d;
    vector<T>F,Finv,Inv,R,L;
    lagrange_interpolation(int D){
        d=D;
        F.resize(d+1);
        Finv.resize(d+1);
        Inv.resize(d+1);
        R.resize(d+1);
        L.resize(d+1);
    }
    void set(vector<T>f){
        Finv[0]=1;
        F[0]=f[0];
        for(int i=1;i<=d;i++){
            F[i]=f[i];
            Inv[i]=(i==1)?1:MOD-Inv[MOD%i]*(MOD/i)%MOD;
            Finv[i]=Finv[i-1]*Inv[i]%MOD;
        }
    }
    T value(T N){
        R[0]=L[d]=1;
        for(int i=1;i<=d;i++){
            R[i]=R[i-1]*(N+1-i)%MOD;
            L[d-i]=L[d-i+1]*(N-d-1+i)%MOD;
        }
        T v=0;
        for(int i=0;i<=d;i++){
            T c=(((F[i]*R[i]%MOD*L[i])%MOD)*Finv[i]%MOD)*Finv[d-i]%MOD;
            if((d-i)%2==0)v+=c;
            else v-=c;
            v=(v+MOD)%MOD;
        }
        return v;
    }
};

ll power(ll a, ll b){
    ll re = 1;
    while (b > 0){
        if (b & 1) re = (re * a) % MOD;
        a = (a * a) % MOD;
        b >>= 1;
    }
    return re;
}

const ll fac[1000]={
1,373341033,45596018,834980587,623627864,428937595,442819817,499710224,833655840,83857087,295201906,788488293,671639287,849315549,597398273,813259672,732727656,244038325,122642896,310517972,160030060,483239722,683879839,712910418,384710263,433880730,844360005,513089677,101492974,959253371,957629942,678615452,34035221,56734233,524027922,31729117,102311167,330331487,8332991,832392662,545208507,594075875,318497156,859275605,300738984,767818091,864118508,878131539,316588744,812496962,213689172,584871249,980836133,54096741,417876813,363266670,335481797,730839588,393495668,435793297,760025067,811438469,720976283,650770098,586537547,117371703,566486504,749562308,708205284,932912293,939830261,983699513,206579820,301188781,593164676,770845925,247687458,41047791,266419267,937835947,506268060,6177705,936268003,166873118,443834893,328979964,470135404,954410105,117565665,832761782,39806322,478922755,394880724,821825588,468705875,512554988,232240472,876497899,356048018,895187265,808258749,575505950,68190615,939065335,552199946,694814243,385460530,529769387,640377761,916128300,440133909,362216114,826373774,502324157,457648395,385510728,904737188,78988746,454565719,623828097,686156489,713476044,63602402,570334625,681055904,222059821,477211096,343363294,833792655,461853093,741797144,74731896,930484262,268372735,941222802,677432735,474842829,700451655,400176109,697644778,390377694,790010794,360642718,505712943,946647976,339045014,715797300,251680896,70091750,40517433,12629586,850635539,110877109,571935891,695965747,634938288,69072133,155093216,749696762,963086402,544711799,724471925,334646013,574791029,722417626,377929821,743946412,988034679,405207112,18063742,104121967,638607426,607304611,751377777,35834555,313632531,18058363,656121134,40763559,562910912,495867250,48767038,210864657,659137294,715390025,865854329,324322857,388911184,286059202,636456178,421290700,832276048,726437551,526417714,252522639,386147469,674313019,274769381,226519400,272047186,117153405,712896591,486826649,119444874,338909703,18536028,41814114,245606459,140617938,250512392,57084755,157807456,261113192,40258068,194807105,325341339,884328111,896332013,880836012,737358206,202713771,785454372,399586250,485457499,640827004,546969497,749602473,159788463,159111724,218592929,675932866,314795475,811539323,246883213,696818315,759880589,4302336,353070689,477909706,559289160,79781699,878094972,840903973,367416824,973366814,848259019,462421750,667227759,897917455,81800722,956276337,942686845,420541799,417005912,272641764,941778993,217214373,192220616,267901132,50530621,652678397,354880856,164289049,781023184,105376215,315094878,607856504,733905911,457743498,992735713,35212756,231822660,276036750,734558079,424180850,433186147,308380947,18333316,12935086,351491725,655645460,535812389,521902115,67016984,48682076,64748124,489360447,361275315,786336279,805161272,468129309,645091350,887284732,913004502,358814684,281295633,328970139,395955130,164840186,820902807,761699708,246274415,592331769,913846362,866682684,600130702,903837674,529462989,90612675,526540127,533047427,110008879,674279751,801920753,645226926,676886948,752481486,474034007,457790341,166813684,287671032,188118664,244731384,404032157,269766986,423996017,182948540,356801634,737863144,652014069,206068022,504569410,919894484,593398649,963768176,882517476,702523597,949028249,128957299,171997372,50865043,20937461,690959202,581356488,369182214,993580422,193500140,540665426,365786018,743731625,144980423,979536721,773259009,617053935,247670131,843705280,30419459,985463402,261585206,237885042,111276893,488166208,137660292,720784236,244467770,26368504,792857103,666885724,670313309,905683034,259415897,512017253,826265493,111960112,633652060,918048438,516432938,386972415,996212724,610073831,444094191,72480267,665038087,11584804,301029012,723617861,113763819,778259899,937766095,535448641,593907889,783573565,673298635,599533244,655712590,173350007,868198597,169013813,585161712,697502214,573994984,285943986,675831407,3134056,965907646,401920943,665949756,236277883,612745912,813282113,892454686,901222267,624900982,927122298,686321335,84924870,927606072,506664166,353631992,165913238,566073550,816674343,864877926,171259407,908752311,874007723,803597299,613676466,880336545,282280109,128761001,58852065,474075900,434816091,364856903,149123648,388854780,314693916,423183826,419733481,888483202,238933227,336564048,757103493,100189123,855479832,51370348,403061033,496971759,831753030,251718753,272779384,683379259,488844621,881783783,659478190,445719559,740782647,546525906,985524427,548033568,333772553,331916427,752533273,730387628,93829695,655989476,930661318,334885743,466041862,428105027,888238707,232218076,769865249,730641039,616996159,231721356,326973501,426068899,722403656,742756734,663270261,364187931,350431704,671823672,633125919,226166717,386814657,237594135,451479365,546182474,119366536,465211069,605313606,728508871,249619035,663053607,900453742,48293872,229958401,62402409,69570431,71921532,960467929,537087913,514588945,513856225,415497414,286592050,645469437,102052166,163298189,873938719,617583886,986843080,962390239,580971332,665147020,88900164,89866970,826426395,616059995,443012312,659160562,229855967,687413213,59809521,398599610,325666688,154765991,159186619,210830877,386454418,84493735,974220646,820097297,2191828,481459931,729073424,551556379,926316039,151357011,808637654,218058015,786112034,850407126,84202800,94214098,30019651,121701603,176055335,865461951,553631971,286620803,984061713,888573766,302767023,977070668,110954576,83922475,51568171,60949367,19533020,510592752,615419476,341370469,912573425,286207526,206707897,384156962,414163604,193301813,749570167,366933789,11470970,600191572,391667731,328736286,30645366,215162519,604947226,236199953,718439098,411423177,803407599,632441623,766760224,263006576,757681534,61082578,681666415,947466395,12206799,659767098,933746852,978860867,59215985,161179205,439197472,259779111,511621808,145770512,882749888,943124465,872053396,631078482,166861622,743415395,772287179,602427948,924112080,385643091,794973480,883782693,869723371,805963889,313106351,262132854,400034567,488248149,265769800,791715397,408753255,468381897,415812467,172922144,64404368,281500398,512318142,288791777,955559118,242484726,536413695,205340854,707803527,576699812,218525078,875554190,46283078,833841915,763148293,807722138,788080170,556901372,150896699,253151120,97856807,918256774,771557187,582547026,472709375,911615063,743371401,641382840,446540967,184639537,157247760,775930891,939702814,499082462,19536133,548753627,593243221,563850263,185475971,687419227,396799323,657976136,864535682,433009242,860830935,33107339,517661450,467651311,812398757,202133852,431839017,709549400,99643620,773282878,290471030,61134552,129206504,929147251,837008968,422332597,353775281,469563025,62265336,835064501,851685235,21197005,264793769,326416680,118842991,84257200,763248924,687559609,150907932,401832452,242726978,766752066,959173604,390269102,992293822,744816299,476631694,177284763,702429415,374065901,169855231,629007616,719169602,564737074,475119050,714502830,40993711,820235888,749063595,239329111,612759169,18591377,419142436,442202439,941600951,158013406,637073231,471564060,447222237,701248503,599797734,577221870,69656699,51052704,6544303,10958310,554955500,943192237,192526269,897983911,961628039,240232720,627280533,710239542,70255649,261743865,228474833,776408079,304180483,63607040,953297493,758058902,395529997,156010331,825833840,539880795,234683685,52626619,751843490,116909119,62806842,574857555,353417551,40061330,822203768,681051568,490913702,9322961,766631257,124794668,37844313,163524507,729108319,490867505,47035168,682765157,53842115,817965276,757179922,339238384,909741023,150530547,158444563,140949492,993302799,551621442,137578883,475122706,443869843,605400098,689361523,769596520,801661499,474900284,586624857,349960501,134084537,650564083,877097974,379857427,887890124,159436401,133274277,986182139,729720334,568925901,459461496,499309445,493171177,460958750,380694152,168836226,840160881,141116880,225064950,109618190,842341383,85305729,759273275,97369807,669317759,766247510,829017039,550323884,261274540,918239352,29606025,870793828,293683814,378510746,367270918,481292028,813097823,798448487,230791733,899305835,504040630,162510533,479367951,275282274,806951470,462774647,56473153,184659008,905122161,664034750,109726629,59372704,325795100,486860143,843736533,924723613,880348000,801252478,616515290,776142608,284803450,583439582,274826676,6018349,377403437,244041569,527081707,544763288,708818585,354033051,904309832,589922898,673933870,682858433,945260111,899893421,515264973,911685911,9527148,239480646,524126897,48259065,578214879,118677219,786127243,869205770,923276513,937928886,802186160,12198440,638784295,34200904,758925811,185027790,80918046,120604699,610456697,573601211,208296321,49743354,653691911,490750754,674335312,887877110,875880304,308360096,414636410,886100267,8525751,636257427,558338775,500159951,696213291,97268896,364983542,937928436,641582714,586211304,345265657,994704486,443549763,207259440,302122082,166055224,623250998,239642551,476337075,283167364,211328914,68064804,950202136,187552679,18938709,646784245,598764068,538505481,610424991,864445053,390248689,278395191,686098470,935957187,868529577,329970687,804930040,84992079,474569269,810762228,573258936,756464212,155080225,286966169,283614605,19283401,24257676,871831819,612689791,846988741,617120754,971716517,979541482,297910784,991087897,783825907,214821357,689498189,405026419,946731704,609346370,707669156,457703127,957341187,980735523,649367684,791011898,82098966,234729712,105002711,130614285,291032164,193188049,363211260,58108651,100756444,954947696,346032213,863300806,36876722,622610957,289232396,667938985,734886266,395881057,417188702,183092975,887586469,83334648,797819763,100176902,781587414,841864935,371674670,18247584,0
};

const int M=1000000;

int main(){
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    ll N,K;
    cin>>N>>K;
    lagrange_interpolation<ll>Lag1(K+1),Lag2(K+2);
    vector<ll>dp1(K+2),dp2(K+3);
    for(int n=1;n<=K+1;n++){
        dp1[n]=(dp1[n-1]+power(n,K))%MOD;
    }
    for(int n=1;n<=K+2;n++){
        dp2[n]=(dp2[n-1]+power(n,K+1))%MOD;
    }
    Lag1.set(dp1);
    Lag2.set(dp2);
    ll ans=2*fac[(N-1)/M]%MOD;
    for(int i=((N-1)/M)*M+1;i<=N-1;i++)ans=(ans*i)%MOD;
    ans=(ans*(N*Lag1.value(N-1)%MOD-Lag2.value(N-1)))%MOD;
    if(ans<0)ans+=MOD;
    cout<<ans<<"\n";
}
0