結果

問題 No.3478 XOR-Folding Primes
コンテスト
ユーザー hos.lyric
提出日時 2026-03-20 21:44:40
言語 C++14
(gcc 15.2.0 + boost 1.89.0)
コンパイル:
g++-15 -O2 -lm -std=c++14 -Wuninitialized -DONLINE_JUDGE -o a.out _filename_
実行:
./a.out
結果
AC  
実行時間 415 ms / 4,000 ms
コード長 6,861 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 1,510 ms
コンパイル使用メモリ 148,832 KB
実行使用メモリ 121,108 KB
最終ジャッジ日時 2026-03-20 21:44:46
合計ジャッジ時間 5,230 ms
ジャッジサーバーID
（参考情報） 		judge3_0 / judge2_1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 8
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 #
raw source code 

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#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 T> ostream &operator<<(ostream &os, const vector<T> &as);
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>;


vector<Mint> findLinearRecurrence(const vector<Mint> &as) {
  const int n = as.size();
  int d = 0, m = 0;
  vector<Mint> cs(n + 1, 0), bs(n + 1, 0);
  cs[0] = bs[0] = 1;
  Mint invBef = 1;
  for (int i = 0; i < n; ++i) {
    ++m;
    Mint dif = as[i];
    for (int j = 1; j < d + 1; ++j) dif += cs[j] * as[i - j];
    if (dif.x != 0) {
      auto csDup = cs;
      const Mint r = dif * invBef;
      for (int j = m; j < n; ++j) cs[j] -= r * bs[j - m];
      if (2 * d <= i) {
        d = i + 1 - d;
        m = 0;
        bs = csDup;
        invBef = dif.inv();
      }
    }
  }
  cs.resize(d + 1);
  return cs;
}

// x^e mod rev(cs)
vector<Mint> powerRev(const vector<Mint> &cs, Int e) {
  assert(!cs.empty());
  assert(cs[0] == 1);
  const int d = (int)cs.size() - 1;
  if (d == 0) return {};
  if (d == 1) return {(-cs[1]).pow(e)};
  auto mul = [&](const vector<Mint> &fs, const vector<Mint> &gs) {
    vector<Mint> hs(d + d - 1, 0);
    for (int i = 0; i < d; ++i) for (int j = 0; j < d; ++j) {
      hs[i + j] += fs[i] * gs[j];
    }
    for (int i = d + d - 1; --i >= d; ) {
      for (int j = 1; j <= d; ++j) {
        hs[i - j] -= cs[j] * hs[i];
      }
    }
    hs.resize(d);
    return hs;
  };
  vector<Mint> xs(d, 0), ys(d, 0);
  xs[1] = 1;
  ys[0] = 1;
  for (; ; xs = mul(xs, xs)) {
    if (e & 1) ys = mul(ys, xs);
    if (!(e >>= 1)) break;
  }
  return ys;
}

Mint linearRecurrenceAt(const vector<Mint> &as, const vector<Mint> &cs, Int e) {
  assert(!cs.empty());
  assert(cs[0] == 1);
  const int d = (int)cs.size() - 1;
  assert((int)as.size() >= d);
  const auto fs = powerRev(cs, e);
  Mint ans = 0;
  for (int i = 0; i < d; ++i) {
    ans += fs[i] * as[i];
  }
  return ans;
}


constexpr int LIM = 10'000'010;
int lpf[LIM];
int pi[LIM], twin[LIM];

int main() {
  for (int p = 2; p < LIM; ++p) lpf[p] = p;
  for (int p = 2; p < LIM; ++p) if (lpf[p] == p) {
    for (int n = p; n < LIM; n += p) chmin(lpf[n], p);
  }
  for (int p = 2; p < LIM; ++p) if (lpf[p] == p) {
    ++pi[p];
    const int q = p ^ 2;
    if (2 < q && q < p && lpf[q] == q) ++twin[p];
  }
  for (int n = 2; n < LIM; ++n) {
    pi[n] += pi[n - 1];
    twin[n] += twin[n - 1];
  }
  
  for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    int N, M;
    scanf("%d%d", &N, &M);
// cerr<<N<<" "<<M<<": "<<pi[M]<<" "<<twin[M]<<endl;
    
    Mint ans = 0;
    if (N == 1) {
      ans += pi[M];
    } else {
      constexpr int LEN = 10;
      vector<Mint> fs(LEN, 0), gs(LEN, 0), as(LEN, 0);
      const Mint t = 2 * twin[M];
      fs[1] += 1;
      gs[1] += t;
      for (int n = 1; n < LEN - 1; ++n) {
        gs[n + 1] += fs[n] * t;
        fs[n + 1] += gs[n];
        gs[n + 1] += gs[n];
      }
      for (int n = 0; n < LEN; ++n) as[n] = fs[n] + gs[n];
      const auto cs = findLinearRecurrence(as);
// cerr<<as<<" "<<cs<<endl;
      ans += linearRecurrenceAt(as, cs, N);
    }
    printf("%u\n", ans.x);
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}
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