#1089439 (C++14) No.1482 Swap Many Permutations

• 問題: No.1482 Swap Many Permutations
• ユーザー: hos.lyric
• 提出日時: 2025-05-31 11:08:56
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 35 ms / 2,000 ms
• コード長: 10,004 bytes
• コンパイル時間: 1,224 ms
• コンパイル使用メモリ: 117,560 KB
• 実行使用メモリ: 7,848 KB
• 最終ジャッジ日時: 2025-05-31 11:09:02
• 合計ジャッジ時間: 6,189 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

ファイルパターン	結果
sample	AC * 2
other	AC * 45

コンパイルメッセージ

main.cpp: In function ‘int main()’:
main.cpp:239:12: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  239 |       scanf("%u%u", &B[i].x, &C[i].x);
      |       ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~

ソースコード

#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 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; }
};
////////////////////////////////////////////////////////////////////////////////

#define ModInt ModIntR
////////////////////////////////////////////////////////////////////////////////
// Barrett
struct ModInt {
  static unsigned M;
  static unsigned long long NEG_INV_M;
  static void setM(unsigned m) { M = m; NEG_INV_M = -1ULL / M; }
  unsigned x;
  ModInt() : x(0U) {}
  ModInt(unsigned x_) : x(x_ % M) {}
  ModInt(unsigned long long x_) : x(x_ % M) {}
  ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  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) {
    const unsigned long long y = static_cast<unsigned long long>(x) * a.x;
    const unsigned long long q = static_cast<unsigned long long>((static_cast<unsigned __int128>(NEG_INV_M) * y) >> 64);
    const unsigned long long r = y - M * q;
    x = r - M * (r >= 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; }
};
unsigned ModInt::M;
unsigned long long ModInt::NEG_INV_M;
// !!!Use ModInt::setM!!!
////////////////////////////////////////////////////////////////////////////////
#undef ModInt

using Mint998 = ModInt<998244353>;
using MintM = ModIntR;

constexpr int LIM_INV = 200'010;
Mint998 inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint998::M / i) * inv[Mint998::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint998 binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}

////////////////////////////////////////////////////////////////////////////////

// M: prime
MintM primitiveRoot() {
  const unsigned M = MintM::M;
  vector<unsigned> ds;
  {
    unsigned m = M - 1;
    for (unsigned q = 2; q * q <= m; ++q) if (m % q == 0) {
      do { m /= q; } while (m % q == 0);
      ds.push_back((M - 1) / q);
    }
    if (m > 1) ds.push_back((M - 1) / m);
  }
  for (unsigned a = 1; a < M; ++a) {
    const MintM g = a;
    if ([&]() -> bool {
      for (const unsigned d : ds) if (g.pow(d).x == 1) return false;
      return true;
    }()) {
      return g;
    }
  }
  assert(false);
}

/*
  >= 3 perms
    p q p^-1 q^-1
    p   p^-1     
      q      q^-1
    generates A_M
  
  parity of (u -> b + c u)
  M = 2:
    (b, c) = (0, 1): even
    (b, c) = (1, 1): odd
  M != 2:
    c = 1:
      b = 0: M cycles; even
      b != 0: 1 cycle: even
    c != 1:
      1 fixed point
      (M-1)/ord(c) cycles of size ord(c)
      even <=> c: quad. residue
  
  L := M(M-1)/2
    all even candidates
    all odd candidates
  (1+x)^L (1+tx)^L mod (1-t^2)
  = (1/2) ((1+x)^2L +- (1+x)^L (1-x)^L)
*/

int N, M;
vector<MintM> B, C;

MintM G;
vector<MintM> Exp;
vector<int> Log;

int parity(MintM b, MintM c) {
  if (M == 2) return b.x;
  return Log[c.x] & 1;
}

int main() {
  prepare();
  
  for (; ~scanf("%d%d", &N, &M); ) {
    MintM::setM(M);
    B.resize(N);
    C.resize(N);
    for (int i = 0; i < N; ++i) {
      scanf("%u%u", &B[i].x, &C[i].x);
    }
    
    G = primitiveRoot();
    Exp.resize(M);
    Exp[0] = 1;
    for (int i = 1; i < M; ++i) Exp[i] = Exp[i - 1] * G;
    Log.assign(M, -1);
    for (int i = 0; i < M - 1; ++i) Log[Exp[i].x] = i;
// cerr<<"Exp = "<<Exp<<endl;
    
    const Int L = (Int)M*(M-1) / 2;
    vector<Mint998> fs(N + 1, 0), gs(N + 1, 0);
    {
      Mint998 bn = 1;
      for (int i = 0; i <= N; ++i) {
        fs[i] = bn;
        bn *= (2*L - i) * inv[1 + i];
      }
    }
    {
      Mint998 bn = 1;
      for (int i = 0; i <= N/2; ++i) {
        gs[2*i] = bn * (i&1?-1:+1);
        bn *= (L - i) * inv[1 + i];
      }
    }
// cerr<<"fs = "<<fs<<endl;
// cerr<<"gs = "<<gs<<endl;
    
    int now = 0;
    for (int n = 1; n <= N; ++n) {
      const int s = parity(B[n - 1], C[n - 1]);
// cerr<<B[n-1]<<" "<<C[n-1]<<": "<<s<<endl;
      now ^= s;
      Mint998 ans;
      if (n == 1) {
        ans = 1;
      } else if (n == 2) {
        ans = (B[0] == B[1] && C[0] == C[1]) ? 0 : ((Int)M*(M-1));
      } else {
        ans = now ? (fs[n] - gs[n]) : (fs[n] + gs[n]);
        ans /= 2;
        ans *= fac[n];
      }
      printf("%u\n", ans.x);
    }
  }
  return 0;
}