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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#183947#4898. 基础图论练习题hos_lyric40 90ms6032kbC++147.6kb2023-09-20 02:17:372023-09-20 02:17:37

Judging History

你现在查看的是最新测评结果

  • [2023-09-20 02:17:37]
  • 评测
  • 测评结果:40
  • 用时:90ms
  • 内存:6032kb
  • [2023-09-20 02:17:37]
  • 提交

answer

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;

int root(vector<int> &uf, int u) {
  return (uf[u] < 0) ? u : (uf[u] = root(uf, uf[u]));
}
bool connect(vector<int> &uf, int u, int v) {
  u = root(uf, u);
  v = root(uf, v);
  if (u == v) return false;
  if (uf[u] > uf[v]) swap(u, v);
  uf[u] += uf[v];
  uf[v] = u;
  return true;
}


Int N;
int A, B;
vector<Int> D;
vector<int> X;
vector<Int> U, V;
vector<int> W;

vector<pair<int, int>> es;


namespace brute {
constexpr int F = 19;
vector<int> ufs[F];

// (u, v), (u + 1, v + 1), ..., (u + 2^f-1, v + 2^f-1)
int rec(int f, int u, int v) {
  int ret = 0;
  if (connect(ufs[f], u, v)) {
    if (f) {
      ret += rec(f - 1, u, v);
      ret += rec(f - 1, u + (1 << (f-1)), v + (1 << (f-1)));
    } else {
      ret += 1;
    }
  }
  return ret;
}

Mint run() {
  for (int f = 0; f < F; ++f) {
    ufs[f].assign(N, -1);
  }
  Mint ans = 0;
  for (const auto &e : es) {
    int num = 0;
    if (e.second < A) {
      const int a = e.second;
      const int f = 31 - __builtin_clz(N - D[a]);
      num += rec(f, 0, D[a]);
      num += rec(f, N - D[a] - (1 << f), N - (1 << f));
    } else {
      const int b = e.second - A;
      num += rec(0, U[b], V[b]);
    }
// cerr<<e<<": "<<num<<endl;
    ans += Mint(e.first) * num;
  }
  return ans;
}
}  // brute


namespace fast {
// vertex 0, ..., n-1
struct HugeGraph {
  Int n;
  vector<Int> ds;
  explicit HugeGraph(Int n_ = 0) : n(n_) {}
  // add edges (u, u + d) for 0 <= u < n - d
  void add(Int d) {
    assert(1 <= d); assert(d < n);
    ds.push_back(d);
  }
  // (# of connected components, component representatives for us)
  // reduce ds so that |ds| <= 2 log_2(min ds) + 1, representing the same graph
  pair<Int, vector<Int>> run(vector<Int> us) {
    Int off = 0;
    priority_queue<pair<Int, Int>, vector<pair<Int, Int>>, greater<pair<Int, Int>>> que;
    for (const Int d : ds) que.emplace(d, d);
    ds.clear();
    // reduce the problem to the graph on [0, nn) with d \in que (with offset)
    Int nn = n, c = 0;
    for (; ; ) {
      if (que.empty()) {
        c += nn;
        break;
      }
      const Int d0 = que.top().first + off;
      const Int save0 = que.top().second;
      que.pop();
      if (d0 == 0) {
        continue;
      }
      ds.push_back(save0);
      for (Int &u : us) if (u < nn) u %= d0;
      if (que.empty()) {
        c += d0;
        break;
      }
      const Int d1 = que.top().first + off;
      const Int k = d1 / d0;
      nn -= d0 * k;
      if (nn < d0) c += (d0 - nn);
      off -= d0 * k;
      if (d0 < nn) que.emplace(d0 - off, save0);
    }
    return make_pair(c, us);
  }
};

Mint run() {
  vector<int> as;
  for (const auto &e : es) if (e.second < A) {
    as.push_back(e.second);
  }
  
  // MST with A-edge
  Mint ans = 0;
  {
    Int numComps = N;
    HugeGraph hg(N);
    for (const int a : as) {
      hg.add(D[a]);
      const Int res = hg.run({}).first;
      ans += Mint(X[a]) * (numComps - res);
      numComps = res;
    }
  }
  
  // TODO: virtual tree
  
  return ans;
}
}  // fast


int main() {
  for (; ~scanf("%lld%d%d", &N, &A, &B); ) {
    D.resize(A);
    X.resize(A);
    for (int a = 0; a < A; ++a) {
      scanf("%lld%d", &D[a], &X[a]);
    }
    U.resize(B);
    V.resize(B);
    W.resize(B);
    for (int b = 0; b < B; ++b) {
      scanf("%lld%lld%d", &U[b], &V[b], &W[b]);
    }
    
    es.resize(A + B);
    for (int a = 0; a < A; ++a) {
      es[a] = make_pair(X[a], a);
    }
    for (int b = 0; b < B; ++b) {
      es[A + b] = make_pair(W[b], A + b);
    }
    sort(es.begin(), es.end());
    
cerr<<"N = "<<N<<", A = "<<A<<", B = "<<B<<endl;
// cerr<<"es = "<<es<<endl;
    
    const Mint ans = fast::run();
    printf("%u\n", ans.x);
#ifdef LOCAL
if(N<=200'000){
 const Mint brt=brute::run();
 if(brt!=ans)cerr<<"brt = "<<brt<<endl;
if(B==0)
 assert(brt==ans);
}
#endif
  }
  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Subtask #1:

score: 0
Wrong Answer

Test #1:

score: 0
Wrong Answer
time: 12ms
memory: 4712kb

input:

161199 9 46510
147335 540442844
159493 801351455
149342 821625305
128476 843250712
95524 275754315
139315 106523502
93575 680460786
155498 328812257
146020 410466645
79992 141967 50596784
152210 68644 268349216
72549 96959 42994091
93869 27394 945120577
2909 81886 270684270
12735 35026 871917997
974...

output:

751220930

result:

wrong answer 1st numbers differ - expected: '359714743', found: '751220930'

Subtask #2:

score: 0
Skipped

Dependency #1:

0%

Subtask #3:

score: 6
Accepted

Test #11:

score: 6
Accepted
time: 1ms
memory: 4100kb

input:

569435269457904707 2 0
490445920091092693 772271583
144842828305643603 609043885

output:

884694794

result:

ok 1 number(s): "884694794"

Test #12:

score: 0
Accepted
time: 0ms
memory: 3812kb

input:

946929772456816659 2 0
589193907831915013 196301185
485768367910597533 207014034

output:

790540706

result:

ok 1 number(s): "790540706"

Test #13:

score: 0
Accepted
time: 0ms
memory: 3808kb

input:

693038683299151358 2 0
654733556025919068 724998910
450253521190874799 187460097

output:

122292064

result:

ok 1 number(s): "122292064"

Test #14:

score: 0
Accepted
time: 0ms
memory: 4068kb

input:

572269482188906358 2 0
545978502848607475 331750201
488577730099900109 477584735

output:

429885702

result:

ok 1 number(s): "429885702"

Test #15:

score: 0
Accepted
time: 0ms
memory: 3840kb

input:

984888155303961325 2 0
421568681423492040 823358650
324408005979881943 905919848

output:

551223124

result:

ok 1 number(s): "551223124"

Test #16:

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

input:

968068649251960108 2 0
932666179822285222 303897491
422068063538287737 405622211

output:

516717723

result:

ok 1 number(s): "516717723"

Test #17:

score: 0
Accepted
time: 0ms
memory: 3812kb

input:

973235486287221374 2 0
604729607242747292 566399250
440704799734330948 93237801

output:

772791524

result:

ok 1 number(s): "772791524"

Test #18:

score: 0
Accepted
time: 0ms
memory: 3776kb

input:

980842002786834388 2 0
921076927921054095 989436809
917078581302025088 354268450

output:

387335763

result:

ok 1 number(s): "387335763"

Test #19:

score: 0
Accepted
time: 0ms
memory: 3792kb

input:

584600268153835325 2 0
436736455094118542 788823700
379215887395241676 440751386

output:

178749302

result:

ok 1 number(s): "178749302"

Test #20:

score: 0
Accepted
time: 0ms
memory: 3808kb

input:

984888155303961325 2 0
421568681423492040 823358650
324408005979881943 905919848

output:

551223124

result:

ok 1 number(s): "551223124"

Subtask #4:

score: 0
Wrong Answer

Dependency #3:

100%
Accepted

Test #21:

score: 0
Wrong Answer
time: 16ms
memory: 4468kb

input:

569435269457904707 2 48002
490445920091092693 772271583
144842828305643603 609043885
71626464779726163 20936760728342582 933619218
254533877531926689 561120543297327423 444805145
102181371350776436 64807827761321835 63236550
442490347461393187 274703226312639148 379888813
153103619447430279 56932615...

output:

884694794

result:

wrong answer 1st numbers differ - expected: '264605976', found: '884694794'

Subtask #5:

score: 12
Accepted

Test #31:

score: 12
Accepted
time: 2ms
memory: 4120kb

input:

755526150476311190 942 0
492334667739348527 1
755523898623296976 1
532486636690994793 1
755526150476030559 1
755526150476249097 1
502164090270592200 1
657422656495814703 1
487200614853438190 1
311037325561173142 1
755526150475651155 1
125287404340238660 1
755524914808674090 1
755526150476177007 1
75...

output:

546044429

result:

ok 1 number(s): "546044429"

Test #32:

score: 0
Accepted
time: 2ms
memory: 3780kb

input:

507397654005748030 973 0
507391491616563534 1
486814015790119176 1
333131389050214032 1
363564475994643564 1
465930313898633808 1
139522156177690314 1
507395579080257474 1
86630001225723132 1
507395634795467574 1
507396923359845774 1
472957579895774142 1
211220548093936200 1
507397483302327114 1
507...

output:

873803086

result:

ok 1 number(s): "873803086"

Test #33:

score: 0
Accepted
time: 0ms
memory: 4084kb

input:

603106685583649335 921 0
550056634223640253 1
603106685583649293 1
603106685583647605 1
603106685583643690 1
603106685583647260 1
603106685583645101 1
603106685583206332 1
603106685583646490 1
579053271797467737 1
603106685567627560 1
392817087439609936 1
603106685583643465 1
603106685583648090 1
60...

output:

249400664

result:

ok 1 number(s): "249400664"

Test #34:

score: 0
Accepted
time: 1ms
memory: 3888kb

input:

548596182165075765 943 0
548596176080168583 1
548596182156180063 1
312480420249896937 1
548596163341594933 1
526283600729694623 1
548596158109050143 1
403131997716059924 1
434962771902913720 1
503166563025971068 1
334309818515550442 1
548596177929282553 1
548596181450546783 1
548596147814225823 1
54...

output:

315888763

result:

ok 1 number(s): "315888763"

Test #35:

score: 0
Accepted
time: 0ms
memory: 3836kb

input:

757339678164545873 914 0
639318686980737134 1
746121423482808728 1
757339678163450618 1
742690258664301578 1
615075436001700347 1
735156649863536078 1
748312116661086428 1
720777012721160772 1
733811525870561678 1
746526366212816378 1
743741354498887825 1
753440640705502328 1
735178291510182878 1
72...

output:

748030011

result:

ok 1 number(s): "748030011"

Test #36:

score: 0
Accepted
time: 1ms
memory: 3888kb

input:

678523609535069397 961 0
678523501457247993 1
678341707003179753 1
678213366219732921 1
596032992350559535 1
595323423910072641 1
178264171486256288 1
678331675351935897 1
353022445409011341 1
653752496830522075 1
662470342111950027 1
587709190707850701 1
678270056924891769 1
677027683908676175 1
67...

output:

562697340

result:

ok 1 number(s): "562697340"

Test #37:

score: 0
Accepted
time: 1ms
memory: 4132kb

input:

657959922343486841 902 0
650132742778059115 1
105135315791795180 1
438709014360864607 1
545602442587344080 1
657551739592023011 1
656791446287459707 1
657959922133303499 1
647469446648658309 1
657959922343384019 1
657959922221719769 1
336017444559583475 1
657959922253125629 1
655097797158940969 1
19...

output:

300994893

result:

ok 1 number(s): "300994893"

Test #38:

score: 0
Accepted
time: 1ms
memory: 3840kb

input:

545476271566415902 948 0
502943849064064720 1
545153141190505744 1
493528954491284005 1
487490221799012640 1
391805643829976272 1
545466964425150144 1
545474613254014704 1
545475659935859328 1
48415031136648176 1
545475230527923072 1
545472466214333424 1
545475176851931040 1
405305381846539616 1
393...

output:

621606394

result:

ok 1 number(s): "621606394"

Test #39:

score: 0
Accepted
time: 1ms
memory: 3908kb

input:

768089367882777564 903 0
768042195730743057 1
624180099065408353 1
677932298998893337 1
761912479820021969 1
373002333986242953 1
681859753068860049 1
768089367882777309 1
580672767835556559 1
768089367882750069 1
51197080622037114 1
737402458661389169 1
768089367882765501 1
707354099585711345 1
768...

output:

319523314

result:

ok 1 number(s): "319523314"

Test #40:

score: 0
Accepted
time: 2ms
memory: 4128kb

input:

803879216581914933 998 0
498552666676978841 1
803189592600095992 1
803577182309491044 1
803875534594601716 1
803827683448699636 1
803767099629307124 1
803775818980883188 1
803799950365214452 1
803816279020876020 1
803806021800931060 1
803585821604611604 1
695090981117645328 1
803690137369875484 1
68...

output:

867132754

result:

ok 1 number(s): "867132754"

Subtask #6:

score: 0
Wrong Answer

Dependency #3:

100%
Accepted

Dependency #5:

100%
Accepted

Test #41:

score: 0
Wrong Answer
time: 2ms
memory: 3836kb

input:

658450692215768892 966 184
215944253331969524 463889684
658450636472429991 583551110
658450692215733673 179443509
658450692215624997 605779678
508574445107762299 859274405
658450681194937638 515630669
63736085272552748 994573345
354907806666837319 932072760
658450692214054043 663256872
6584506911545...

output:

615274238

result:

wrong answer 1st numbers differ - expected: '12943668', found: '615274238'

Subtask #7:

score: 12
Accepted

Dependency #3:

100%
Accepted

Dependency #5:

100%
Accepted

Test #51:

score: 12
Accepted
time: 59ms
memory: 4836kb

input:

571630416836886394 47168 0
96863681397862733 975125142
356044822253140262 598706048
515453346882217082 780566337
310612673285348975 628963074
470413750105710996 521531320
485023891192396182 511014543
294586905153825661 925671185
571630416738335094 158726562
185789055211250703 954614799
3548394816997...

output:

563260749

result:

ok 1 number(s): "563260749"

Test #52:

score: 0
Accepted
time: 57ms
memory: 4628kb

input:

841161310096886484 47782 0
695723253916094448 724478598
540665669817327612 824722094
841159307153505572 358568703
420009767990047350 208597811
841157041808575787 461740092
841153463198963867 569722258
841155889630106597 515332698
835476875635312659 636252803
841161310096575364 268569091
665233067738...

output:

178000363

result:

ok 1 number(s): "178000363"

Test #53:

score: 0
Accepted
time: 51ms
memory: 4688kb

input:

539025190773540771 46142 0
539025114552193483 750084891
539025146939174001 208399611
539025142948200821 59628495
539025167040882541 187485048
297804195276627820 596910027
539025036251289721 292620891
539025176171348121 25151122
419197658222546676 541151443
539025182999530881 170481735
94373350744432...

output:

792619156

result:

ok 1 number(s): "792619156"

Test #54:

score: 0
Accepted
time: 69ms
memory: 4612kb

input:

705921968914365511 47716 0
705921968910682250 37456241
216562629047838980 788958895
705921968888183480 220262214
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705921968902391426 525007326
705921968898107858 563844710
45377210899051...

output:

441700676

result:

ok 1 number(s): "441700676"

Test #55:

score: 0
Accepted
time: 90ms
memory: 4672kb

input:

564133086769866350 48875 0
563437196556182544 261486038
560294783129522064 324772044
556631029930923984 145670740
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473151054735727950 815276832
549167714478150...

output:

310639483

result:

ok 1 number(s): "310639483"

Test #56:

score: 0
Accepted
time: 61ms
memory: 4688kb

input:

936756643107884507 47057 0
936756549937799391 463453118
936756642116110143 96749536
936756552075454317 459354765
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936756643107883335 82112034
8680557778246200...

output:

628129359

result:

ok 1 number(s): "628129359"

Test #57:

score: 0
Accepted
time: 61ms
memory: 4816kb

input:

702873086596726417 46921 0
702873084504467311 435498634
299151456816761100 696668178
702873086593780755 188996895
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480867097500933640 624812518
70287308659425...

output:

296470561

result:

ok 1 number(s): "296470561"

Test #58:

score: 0
Accepted
time: 74ms
memory: 4552kb

input:

696868150883245690 48306 0
476810224399322700 854659018
464195603276193600 304310171
446344869551578397 871173576
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263903781116001600 148139221
42026490439052...

output:

178187268

result:

ok 1 number(s): "178187268"

Test #59:

score: 0
Accepted
time: 67ms
memory: 4872kb

input:

995646392343469795 49194 0
995646392329767108 312459955
995646392334135924 245193472
995646392331093996 299744392
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728936689913383683 819169473
714935731010...

output:

664181186

result:

ok 1 number(s): "664181186"

Test #60:

score: 0
Accepted
time: 88ms
memory: 4596kb

input:

802473733444905042 48027 0
415952639582201792 589867404
802473733444442582 39725642
446316590121917984 571300735
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437186563439513194 897704884
802473733433003...

output:

291107795

result:

ok 1 number(s): "291107795"

Subtask #8:

score: 10
Accepted

Dependency #5:

100%
Accepted

Test #61:

score: 10
Accepted
time: 52ms
memory: 5984kb

input:

716429171502522215 47121 48854
684206275836370608 1
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500447584334752997 1
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29949334130159091...

output:

358321674

result:

ok 1 number(s): "358321674"

Test #62:

score: 0
Accepted
time: 57ms
memory: 6032kb

input:

760962402402047624 47788 46028
760962402400520977 1
146627560121093112 1
552500521368356496 1
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64514813498907734...

output:

397036874

result:

ok 1 number(s): "397036874"

Test #63:

score: 0
Accepted
time: 48ms
memory: 5904kb

input:

823454131189228931 47545 47996
633913455457088435 1
823454131188293887 1
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82345390310591764...

output:

556901026

result:

ok 1 number(s): "556901026"

Test #64:

score: 0
Accepted
time: 51ms
memory: 5868kb

input:

790661905382541343 46638 46580
790661830315353694 1
628815916342495006 1
414195221334706964 1
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22748820983416533...

output:

923583785

result:

ok 1 number(s): "923583785"

Test #65:

score: 0
Accepted
time: 57ms
memory: 5948kb

input:

543995107469111870 46815 49986
543995107427386090 1
543995107385280202 1
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514372106427243364 1
54399510735645175...

output:

549708819

result:

ok 1 number(s): "549708819"

Test #66:

score: 0
Accepted
time: 57ms
memory: 5896kb

input:

973680848449912174 45809 48893
558451142980027913 1
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85928041435845971...

output:

760343391

result:

ok 1 number(s): "760343391"

Test #67:

score: 0
Accepted
time: 56ms
memory: 5804kb

input:

769083325181598713 45572 45512
768897660622302008 1
769083325180938609 1
768647443362725330 1
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518464733738942569...

output:

724840598

result:

ok 1 number(s): "724840598"

Test #68:

score: 0
Accepted
time: 50ms
memory: 5940kb

input:

989697766657099563 45914 49705
219852197404383689 1
491494304787067673 1
872190190190847836 1
887483404175496314 1
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783682329635155073...

output:

478142716

result:

ok 1 number(s): "478142716"

Test #69:

score: 0
Accepted
time: 56ms
memory: 5744kb

input:

508086302629220899 45255 46961
508086302479732309 1
508086302451729729 1
476932514196496909 1
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28492141885045535...

output:

647915375

result:

ok 1 number(s): "647915375"

Test #70:

score: 0
Accepted
time: 56ms
memory: 5968kb

input:

608163868156115674 49705 47751
503333959958709384 1
421780903089450717 1
555039048741370741 1
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48888827368907290...

output:

64753822

result:

ok 1 number(s): "64753822"

Subtask #9:

score: 0
Skipped

Dependency #1:

0%