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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#120139#6187. Digit Sum Problemhos_lyricAC ✓594ms79368kbC++148.1kb2023-07-06 14:12:162023-07-06 14:12:17

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.
  • [2023-07-06 14:12:17]
  • 评测
  • 测评结果:AC
  • 用时:594ms
  • 内存:79368kb
  • [2023-07-06 14:12:16]
  • 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 <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; }

////////////////////////////////////////////////////////////////////////////////
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 main() {
  Int N;
  Mint A, B[2];
  
  for (; ~scanf("%lld%u%u%u", &N, &A.x, &B[0].x, &B[1].x); ) {
    const Int sqrtN = sqrt((long double)N);
    
    Int m[2] = {1, 1};
    m[0] = m[1] = 1;
    // [0][0], [1][1]: offset of the other
    // [0][1], [1][0]: length
    vector<Mint> f[2][2];
    f[0][0] = f[1][1] = {1};
    f[0][1] = f[1][0] = {0, 1};
    
    for (; ; ) {
cerr<<"m = ";pv(m,m+2);
#ifdef LOCAL_
for(int s=0;s<2;++s)for(int t=0;t<2;++t)cerr<<"f["<<s<<"]["<<t<<"] = "<<f[s][t]<<endl;
auto brute=[&](Int r0,Int r1,Int len)->Mint{
 Mint ret=0;
 Mint a=1;
 for(Int i=0;i<len;++i){
  Mint prod=a;
  for(Int x=(r0+i)%m[0];x;x/=2){if(x%2>=1)prod*=B[0];}
  for(Int x=(r1+i)%m[1];x;x/=3){if(x%3>=1)prod*=B[1];if(x%3>=2)prod*=B[1];}
  ret+=prod;
  a*=A;
 }
// cerr<<"  brute "<<r0<<" "<<r1<<" "<<len<<" = "<<ret<<endl;
 return ret;
};
for(int i=0;i<m[1];++i)assert(brute(0,i,m[0])==f[0][0][i]);
for(int i=0;i<m[0];++i)assert(brute(i,0,m[1])==f[1][1][i]);
for(int i=0;i<=min(m[0],m[1]);++i)assert(brute(0,m[1]-i,i)==f[0][1][i]);
for(int i=0;i<=min(m[0],m[1]);++i)assert(brute(m[0]-i,0,i)==f[1][0][i]);
#endif
      
      int s, t;
      Int mm;
      if (m[0] <= m[1]) {
        s = 0;
        t = 1;
        mm = 2 * m[0];
      } else {
        s = 1;
        t = 0;
        mm = 3 * m[1];
      }
      if (mm > sqrtN) {
        break;
      }
      
      vector<Mint> as(min(mm, m[t]) + 1);
      as[0] = 1;
      for (int i = 0; i < min(mm, m[t]); ++i) as[i + 1] = as[i] * A;
      const Mint bs[3] = {1, B[s], B[s] * B[s]};
      
      auto calc = [&](Int Rs, Int rt, Int len) -> Mint {
        Mint ret = 0;
        Mint a = 1;
        Int rs = Rs % m[s];
        for (; len > 0; ) {
          const Int d = min(m[s] - rs, m[t] - rt);
          const Int rrs = ((rs + d == m[s]) ? 0 : (rs + d)); 
          const Int rrt = ((rt + d == m[t]) ? 0 : (rt + d)); 
          assert(rs == 0 || rt == 0);
          assert(rrs == 0 || rrt == 0);
          ret += a * bs[Rs / m[s]] * (
            (rs == 0)
                ? ((rrs == 0) ? f[s][s][rt] : f[s][t][d])
                : ((rrs == 0) ? f[t][s][d] : f[t][t][rs])
          );
          Rs = ((Rs + d) == mm) ? 0 : (Rs + d);
          rs = rrs;
          rt = rrt;
          len -= d;
          a *= as[d];
        }
        return ret;
      };
      
      vector<Mint> g[2][2];
      g[s][s].assign(m[t], 0);
      g[t][t].assign(mm, 0);
      g[s][t].assign(min(mm, m[t]) + 1, 0);
      g[t][s].assign(min(mm, m[t]) + 1, 0);
      for (int i = 0; i < m[t]; ++i) g[s][s][i] = calc(0, i, mm);
      for (int i = 0; i < mm; ++i) g[t][t][i] = calc(i, 0, m[t]);
      for (int i = 0; i <= min(mm, m[t]); ++i) g[s][t][i] = calc(0, m[t] - i, i);
      for (int i = 0; i <= min(mm, m[t]); ++i) g[t][s][i] = calc(mm - i, 0, i);
      
      m[s] = mm;
      for (int ss = 0; ss < 2; ++ss) for (int tt = 0; tt < 2; ++tt) {
        f[ss][tt] = g[ss][tt];
      }
    }
    
    vector<Mint> as(min(m[0], m[1]) + 1);
    as[0] = 1;
    for (int i = 0; i < min(m[0], m[1]); ++i) as[i + 1] = as[i] * A;
    Int lim[2];
    vector<Mint> bs[2];
    for (int s = 0; s < 2; ++s) {
      lim[s] = max(m[s], N / m[s] + 1);
      bs[s].resize(lim[s]);
      bs[s][0] = 1;
      for (int i = 1; i < lim[s]; ++i) {
        bs[s][i] = bs[s][i / ((s == 0) ? 2 : 3)];
        if (s == 0 && i % 2 >= 1) bs[s][i] *= B[s];
        if (s == 1 && i % 3 >= 1) bs[s][i] *= B[s];
        if (s == 1 && i % 3 >= 2) bs[s][i] *= B[s];
      }
    }
    
    Mint ans = 0;
    Mint a = 1;
    for (Int n = 0; n < N + 1; ) {
      const Int d = min(m[0] - n % m[0], m[1] - n % m[1]);
      if (n + d <= N + 1) {
        Mint low;
        if (n % m[0] == 0) {
          if ((n + d) % m[0] == 0) {
            low = f[0][0][n % m[1]];
          } else {
            low = f[0][1][d];
          }
        } else {
          if ((n + d) % m[0] == 0) {
            low = f[1][0][d];
          } else {
            low = f[1][1][n % m[0]];
          }
        }
        ans += a * bs[0][n / m[0]] * bs[1][n / m[1]] * low;
        n += d;
        a *= as[d];
      } else {
        for (; n < N + 1; ++n) {
          ans += a * bs[0][n / m[0]] * bs[0][n % m[0]] * bs[1][n / m[1]] * bs[1][n % m[1]];
          a *= A;
        }
      }
    }
    // n = 0
    ans -= 1;
    printf("%u\n", ans.x);
  }
  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 3660kb

input:

123456 12345 234567 3456789

output:

664963464

result:

ok 1 number(s): "664963464"

Test #2:

score: 0
Accepted
time: 589ms
memory: 79204kb

input:

9876543210987 12816 837595 128478

output:

7972694

result:

ok 1 number(s): "7972694"

Test #3:

score: 0
Accepted
time: 551ms
memory: 77540kb

input:

9196665971964 727160879 966835565 746444639

output:

949890012

result:

ok 1 number(s): "949890012"

Test #4:

score: 0
Accepted
time: 556ms
memory: 77560kb

input:

9361549073598 749653880 965489817 371100607

output:

949904373

result:

ok 1 number(s): "949904373"

Test #5:

score: 0
Accepted
time: 560ms
memory: 77604kb

input:

9567572694963 193332930 544713669 390021151

output:

878781872

result:

ok 1 number(s): "878781872"

Test #6:

score: 0
Accepted
time: 585ms
memory: 78660kb

input:

9769301349033 215825931 425927410 408941695

output:

351574791

result:

ok 1 number(s): "351574791"

Test #7:

score: 0
Accepted
time: 594ms
memory: 79368kb

input:

9975324970399 657749333 5151262 729852127

output:

400022780

result:

ok 1 number(s): "400022780"

Test #8:

score: 0
Accepted
time: 1ms
memory: 3636kb

input:

1 149762920 266126484 107367523

output:

910371791

result:

ok 1 number(s): "910371791"

Test #9:

score: 0
Accepted
time: 156ms
memory: 34984kb

input:

903900971479 969144397 356713678 36786741

output:

414279957

result:

ok 1 number(s): "414279957"

Test #10:

score: 0
Accepted
time: 237ms
memory: 44376kb

input:

1940757501452 72683414 106545701 263512239

output:

786323834

result:

ok 1 number(s): "786323834"

Test #11:

score: 0
Accepted
time: 333ms
memory: 50584kb

input:

2914414844884 174466783 133201789 792227626

output:

187534312

result:

ok 1 number(s): "187534312"

Test #12:

score: 0
Accepted
time: 350ms
memory: 62080kb

input:

3851250038782 553074217 881278164 297532837

output:

847958862

result:

ok 1 number(s): "847958862"

Test #13:

score: 0
Accepted
time: 457ms
memory: 77572kb

input:

4692374803740 352867698 211679787 826248223

output:

426334178

result:

ok 1 number(s): "426334178"

Test #14:

score: 0
Accepted
time: 494ms
memory: 77548kb

input:

5566041306806 454651067 959756163 633543322

output:

842296050

result:

ok 1 number(s): "842296050"

Test #15:

score: 0
Accepted
time: 513ms
memory: 77568kb

input:

6902869060611 556434437 709588186 860268821

output:

897681255

result:

ok 1 number(s): "897681255"

Test #16:

score: 0
Accepted
time: 512ms
memory: 77604kb

input:

7239695301792 356227918 736244273 667563920

output:

726280051

result:

ok 1 number(s): "726280051"

Test #17:

score: 0
Accepted
time: 549ms
memory: 77448kb

input:

8217660029470 458011287 486076297 198034954

output:

967159922

result:

ok 1 number(s): "967159922"