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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#73619#1254. Biggest Set EverupobirWA 632ms4564kbC++145.2kb2023-01-26 19:04:112023-01-26 19:04:14

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-01-26 19:04:14]
  • 评测
  • 测评结果:WA
  • 用时:632ms
  • 内存:4564kb
  • [2023-01-26 19:04:11]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;
using ll = long long int;



//7340033 = 7*2^20, 645922817 = 77*2^23, G = 3
//897581057=107*2^23, 998244353=119*2^23, G = 3
namespace NTT {
vector<int> perm, wp[2]; int root, inv, N, invN;
const int mod = 998244353, G = 3; ///G prim root
int power(int a, int p) {
  int ans = 1;
  while (p) {
    if (p & 1) ans = (1LL*ans*a)%mod;
    a = (1LL*a*a)%mod; p >>= 1;
  } return ans;
}
void precalculate(int n) {
  assert( (n&(n-1)) == 0 && (mod-1)%n==0);
  N = n; invN = power(N, mod-2);
  perm = wp[0] = wp[1] = vector<int>(N);
  perm[0] = 0;
  for (int k=1; k<N; k<<=1)
    for (int i=0; i<k; i++) {
      perm[i] <<= 1; perm[i+k] = 1 + perm[i]; }
  root=power(G,(mod-1)/N); inv=power(root, mod-2);
  wp[0][0]=wp[1][0]=1;
  for (int i=1; i<N; i++) {
    wp[0][i] = (wp[0][i-1]*1LL*root)%mod;
    wp[1][i] = (wp[1][i-1]*1LL*inv)%mod;
  }
}
void fft(vector<int> &v, bool invert = false) {
  if (v.size()!=perm.size())precalculate(v.size());
  for (int i=0; i<N; i++)
    if (i < perm[i])    swap(v[i], v[perm[i]]);

  for (int len = 2; len <= N; len *= 2) {
    for (int i=0, d = N/len; i<N; i+=len) {
      for (int j=0, idx=0; j<len/2; j++, idx+=d) {
        int x=v[i+j], y =
           (wp[invert][idx]*1LL*v[i+j+len/2])%mod;
        v[i+j] = (x+y>=mod ? x+y-mod : x+y);
        v[i+j+len/2] = (x-y>=0 ? x-y : x-y+mod);
      }
    }
  } if (invert) {
    for (int &x : v) x = (x*1LL*invN)%mod; }
}
vector<int> multiply(vector<int> a, vector<int> b){
  int n = 1; while (n < a.size()+ b.size()) n<<=1;
  a.resize(n); b.resize(n);
  fft(a); fft(b);
  for (int i=0;i<n;i++) a[i]=(a[i]*1LL*b[i])%mod;
  fft(a, true); return a;
}

vector<int> conv(vector<int> a, vector<int> b, int NN){
  int n = 1; while (n < a.size()+ b.size()) n<<=1;
  a.resize(n); b.resize(n);
  fft(a); fft(b);
  for (int i=0;i<n;i++) a[i]=(a[i]*1LL*b[i])%mod;

  fft(a, true);

  for(int i = NN; i<a.size(); i++){
    a[i%NN] += a[i];
    if(a[i%NN] >= mod) a[i%NN] -= mod;
  }

  a.resize(NN);

  return a;
}

vector<int> selfconv(vector<int> a, int NN){
  int n = 1; while (n < a.size()+ a.size()) n<<=1;
  a.resize(n);
  fft(a);
  for (int i=0;i<n;i++) a[i]=(a[i]*1LL*a[i])%mod;

  fft(a, true);

  for(int i = NN; i<a.size(); i++){
    a[i%NN] += a[i];
    if(a[i%NN] >= mod) a[i%NN] -= mod;
  }

  a.resize(NN);

  return a;
}


};



const int base = 1e9;
const ll mod = 998244353;

int divide(vector<int>& a, int b){
    int carry = 0;
    for (int i=(int)a.size()-1; i>=0; --i) {
        long long cur = a[i] + carry * 1ll * base;
        a[i] = int (cur / b);
        carry = int (cur % b);
    }
    while (a.size() > 1 && a.back() == 0)
        a.pop_back();

    return carry;
}

vector<int> tonum(string& s){
    vector<int> a;
    for (int i=(int)s.length(); i>0; i-=9)
        if (i < 9)
            a.push_back (atoi (s.substr (0, i).c_str()));
        else
            a.push_back (atoi (s.substr (i-9, 9).c_str()));

    return a;
}

int dp[2][10005];

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);

    int n;
    cin>>n;

    int rem;
    cin>>rem;

    assert(0 <= rem && rem < n && n <= 10000);

    string ss;
    cin>>ss;

    assert(ss.size() <= 100000 && 1 <= ss.size());
    assert(ss[0] != '0');

    for(auto c : ss){
        assert(isdigit(c));
    }

    auto T = tonum(ss);

    auto tmp = T;
    auto kk = divide(tmp, mod-1);

    int pref = divide(T, n);
    auto k = divide(T, mod-1);

    bool is0 = false;
    if(k == 0){
        is0 = true;
    }

    k += mod-1;

    if(k == 0){
        cerr<<"noo"<<endl;
    }

//    pref--;
//    if(pref < 0){
//        pref += n;
//        k--;
//        if(k < 0)
//            k += mod-1;
//    }

//    auto T = stoll(s);
//    auto pref = T % n;
//    T /= n;
//    auto k = T % (mod-1);

    vector<int> P(n), Full(n);
    P[0] = 1;

//    cout<<k<<" "<<pref<<endl;


    dp[0][0] = 1;
    int cur = 0;
    for(int i = 0; i<n; i++){
        cur^=1;
        for(int s = 0; s<n; s++){
            if(s-i >= 0)
                dp[cur][s] = dp[cur^1][s] + dp[cur^1][s-i];
            else
                dp[cur][s] = dp[cur^1][s] + dp[cur^1][s-i+n];

            if(dp[cur][s] >= mod)
                dp[cur][s] -= mod;
        }

        if(i+1 == pref){
            for(int j = 0; j<n; j++)
                P[j] = dp[cur][j];
        }
    }

    for(int i = 0; i<n; i++){
        Full[i] = dp[cur][i];
    }

//    for(int i = 0; i<n; i++)
//        cout<<P[i]<<" ";
//    cout<<endl;
//
//    for(int i = 0; i<n; i++)
//        cout<<Full[i]<<" ";
//    cout<<endl;


    /// FULL^k

    vector<int> ans(n);
    ans[0] = 1;


    while(k && !is0){
        if(k&1){
            ans = NTT::conv(ans, Full, n);
        }
        Full = NTT::selfconv(Full, n);
        k >>= 1;
    }

    ans = NTT::conv(ans, P, n);

    ll sum = 0;
    for(int i = 0; i<n; i++){
        sum = (sum + ans[i]) % mod;
    }

    assert(sum == NTT::power(2, kk));

    assert(ans[rem] >= 0 && ans[rem] < mod);


    cout<<ans[rem]<<endl;





    return 0;
}


Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 3484kb

input:

3 2
5

output:

8

result:

ok single line: '8'

Test #2:

score: 0
Accepted
time: 1ms
memory: 3356kb

input:

1 0
20

output:

1048576

result:

ok single line: '1048576'

Test #3:

score: 0
Accepted
time: 2ms
memory: 3440kb

input:

10 8
97441781169999

output:

39483594

result:

ok single line: '39483594'

Test #4:

score: 0
Accepted
time: 2ms
memory: 3368kb

input:

10 0
73529553919999

output:

913188246

result:

ok single line: '913188246'

Test #5:

score: 0
Accepted
time: 1ms
memory: 3484kb

input:

10 5
7216893652

output:

803006513

result:

ok single line: '803006513'

Test #6:

score: 0
Accepted
time: 0ms
memory: 3468kb

input:

51 4
490466735660935366104362911237439817660296497884511278059120667639249811034386376211440059814876153833104198879999

output:

754741857

result:

ok single line: '754741857'

Test #7:

score: 0
Accepted
time: 2ms
memory: 3448kb

input:

45 0
6216871967465786523158710331777577058507955388049665933617608862925909208090781993189722633093256714163855609550090284484136100755698161980229368887021285893611742334609577808667250730098679567168835635687562524497440298178123243152474212724715349775392879081815671155873083166544656572426801376...

output:

247716490

result:

ok single line: '247716490'

Test #8:

score: 0
Accepted
time: 2ms
memory: 3380kb

input:

123 95
82762777129999

output:

104574851

result:

ok single line: '104574851'

Test #9:

score: 0
Accepted
time: 2ms
memory: 3400kb

input:

100 8
31437474627210849758566270683758273881261075882083602376365854183768172131884521374556483688326470349999

output:

204425046

result:

ok single line: '204425046'

Test #10:

score: 0
Accepted
time: 2ms
memory: 3420kb

input:

101 65
129135732687243444162224693341284265097302999818949156642879266983062901971745283891629743024085567839999

output:

902554661

result:

ok single line: '902554661'

Test #11:

score: 0
Accepted
time: 2ms
memory: 3368kb

input:

102 0
3488151969475412325389878205822308160017247852281650623347454005909349359794006198664575307015721114499999

output:

162486241

result:

ok single line: '162486241'

Test #12:

score: 0
Accepted
time: 10ms
memory: 3564kb

input:

1012 291
7646813626

output:

980146392

result:

ok single line: '980146392'

Test #13:

score: 0
Accepted
time: 1ms
memory: 3364kb

input:

10 1
8252321334895940615769970904772140913784950414733677250236907211278760730743749190165425246198980003063223759998857676592610546612494049860039116369420896260329913339201912705127782100719073680933781912596330763621573961781964610789874205137283507240907978239171437180129623254976853141357534721...

output:

652741132

result:

ok single line: '652741132'

Test #14:

score: 0
Accepted
time: 565ms
memory: 4520kb

input:

10000 7418
3245239614838766441165109131458206859599048822364196500920217765340625035454604743711500986644932444050563968810069079688108908878846571710567968402401812796927116289077099295526340820005662199516680283500266534222567954309211983031474586099314642398538154929871106845369013158161741156285...

output:

698356153

result:

ok single line: '698356153'

Test #15:

score: 0
Accepted
time: 632ms
memory: 4352kb

input:

9999 779
358336376636226042717427621455961243958393374012413730691317569180699582766828947496902145881339115917085532012414592514320100982450700615324388139090946345231102734023340224881463299658303159811283914016535239877151817544726113079790779414960958512664223829472539894897355539363031791406089...

output:

837883243

result:

ok single line: '837883243'

Test #16:

score: 0
Accepted
time: 561ms
memory: 4564kb

input:

10000 0
5959081123960981456052979042226085365217802503520521998482870583390422819313350263042136451463933153462392827184151729621677652847629006369849703956071611814775739516186470151700231702587051465357283648453972097435393937208562095551505345722276019216674741689533178156201652677931133018670075...

output:

924699691

result:

ok single line: '924699691'

Test #17:

score: 0
Accepted
time: 577ms
memory: 4544kb

input:

10000 9535
4529914918413777622528043117043450937202591529390096894597801955131392043838551780190373994052685563959267673748578051484778843491690348530040553041327206108222053240121197654468570203072462947279505179444683716795754611201162765280673498257918169149948361212426058346508829709396950512100...

output:

984036477

result:

ok single line: '984036477'

Test #18:

score: 0
Accepted
time: 529ms
memory: 4332kb

input:

9240 4639
27361723410151521150732754757747824591816341408004277395827380018571695767504374102641417978743103148415278527868597085535196798439563729486914117045504466181228391680543038904853912910914033179148538533773830859471039264891096812737067663728830538925263207278489348217296058385024096176645...

output:

918206285

result:

ok single line: '918206285'

Test #19:

score: 0
Accepted
time: 371ms
memory: 4388kb

input:

8640 0
36542487284167251663740647042989590271004990959161565599035618320359555884164889579638216196822119364835481192513876617252278990351166475479529866772377957875189299536492571051813538976297743058308068985113568320877021600430398281676260145773030952556440352937340499556103082922663344786146031...

output:

183559339

result:

ok single line: '183559339'

Test #20:

score: 0
Accepted
time: 425ms
memory: 4380kb

input:

8400 300
288271854704449002303660023988228953095431900267967796390634942331317772470120001601892932430552455756800781384921666042619127984502628855577098517482540354318793004328371417736520135839821219973136389836602550635594752488595369449820630558647394225301132623150116886896899160930010237898661...

output:

236192822

result:

ok single line: '236192822'

Test #21:

score: 0
Accepted
time: 625ms
memory: 4432kb

input:

9900 7932
60696943972373113723790595629126483514286522739943462090310067978198194825062752363577899690215576140733032790987877947244269329280647842553127506268616051081441746603578834885861401552062986268589398127724619814495854782291653679848340686262859158150894989658137076297136845970234357040248...

output:

957197274

result:

ok single line: '957197274'

Test #22:

score: 0
Accepted
time: 274ms
memory: 4104kb

input:

8064 0
47334321587030653743112677374440705129805126456129176300634909485205142778452960069919888488272962888344558362309553430584472473664877747506095230385831376281275441466113307422446138481496975295148631099507964104577181484367166622611546731949305572711810831571898086598100505274361166695152297...

output:

669865153

result:

ok single line: '669865153'

Test #23:

score: 0
Accepted
time: 331ms
memory: 4156kb

input:

7560 4251
33923778033803241908219943724011782970171842843279830346925914273149746589031596306410354155061775627084155077246765927736846008968413480151788681683200760666695266835650540805104008248152259180695495822884752048464024168111056913040542477162151971025210582160878305329922703362973968810986...

output:

416930414

result:

ok single line: '416930414'

Test #24:

score: 0
Accepted
time: 2ms
memory: 3368kb

input:

1 0
1

output:

2

result:

ok single line: '2'

Test #25:

score: 0
Accepted
time: 1ms
memory: 3384kb

input:

20 0
1

output:

2

result:

ok single line: '2'

Test #26:

score: 0
Accepted
time: 2ms
memory: 3412kb

input:

20 13
1

output:

0

result:

ok single line: '0'

Test #27:

score: 0
Accepted
time: 603ms
memory: 4380kb

input:

10000 4469
9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

output:

290641673

result:

ok single line: '290641673'

Test #28:

score: 0
Accepted
time: 334ms
memory: 4112kb

input:

7560 4041
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

output:

74525042

result:

ok single line: '74525042'

Test #29:

score: 0
Accepted
time: 607ms
memory: 4432kb

input:

9973 5944
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

output:

881015534

result:

ok single line: '881015534'

Test #30:

score: 0
Accepted
time: 524ms
memory: 4376kb

input:

9240 105
999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

output:

971384312

result:

ok single line: '971384312'

Test #31:

score: 0
Accepted
time: 471ms
memory: 4028kb

input:

9240 407
3576

output:

801993513

result:

ok single line: '801993513'

Test #32:

score: -100
Wrong Answer
time: 448ms
memory: 4232kb

input:

9240 551
204209679712117827730880226353510653024223856012233043639816521107053027427255530900909664190550923070609753205194078932813278453978969048551211039657884854091997550079122709572652601873661760656527148885540570009859983720628938737170862051434146563351143193685385454224852792784922646291244...

output:

61877843

result:

wrong answer 1st lines differ - expected: '119770088', found: '61877843'