#1191171 (C++14) No.3753 Certainly a Cretan

• 問題: No.3753 Certainly a Cretan
• ユーザー: hos.lyric
• 提出日時: 2026-10-02 22:25:33
• 言語: C++14 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 167 ms / 2,500 ms
• コード長: 8,684 bytes
• コンパイル時間: 736 ms
• コンパイル使用メモリ: 152,164 KB
• 実行使用メモリ: 59,136 KB
• 最終ジャッジ日時: 2026-10-02 22:25:40
• 合計ジャッジ時間: 5,326 ms
• ジャッジサーバーID （参考情報）: judge4_0 / judge1_0

ファイルパターン	結果
sample	AC * 2
other	AC * 46

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 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>;

constexpr int LIM_INV = 2'000'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::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];
  }
}
Mint 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;
    }
  }
}

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


int N, Q;
char S[1'000'010];

vector<Mint> cat, invCat;

Mint now;
map<int, int> fs;

// S[2j-2] = S[2j-1]: [0, 2j-1) vs j
int equal(int j) {
  assert(1 <= j);
  assert(2*j - 2 < N);
  if (j == 1 || S[2*j - 4] != S[2*j - 2] || (2*j < N && S[2*j - 2] != S[2*j])) {
    return (S[2*j - 2] == 'N') ? j : (j - 1);
  }
  return -1;
}

void update(int j, int val) {
  {
    auto it = fs.find(j);
    if (it != fs.end()) {
      auto itL = it; --itL;
      auto itR = it; ++itR;
      const int l = itL->first;
      const int r = itR->first;
      const int a = itL->second;
      const int b = it ->second;
      const int c = itR->second;
      if (~a && j - l == b - a) now *= invCat[j - l + 1];
      if (~c && r - j == c - b) now *= invCat[r - j + 1];
      if (~a && ~c && r - l == c - a) now *= cat[r - l + 1];
      fs.erase(it);
    }
  }
  if (~val) {
    fs[j] = val;
    auto it = fs.find(j);
    {
      auto itL = it; --itL;
      auto itR = it; ++itR;
      const int l = itL->first;
      const int r = itR->first;
      const int a = itL->second;
      const int b = it ->second;
      const int c = itR->second;
      if (~a && j - l == b - a) now *= cat[j - l + 1];
      if (~c && r - j == c - b) now *= cat[r - j + 1];
      if (~a && ~c && r - l == c - a) now *= invCat[r - l + 1];
    }
  }
}

int main() {
  prepare();
  
  for (; ~scanf("%d%d", &N, &Q); ) {
    scanf("%s", S);
    
    cat.resize(N + 1);
    invCat.resize(N + 1);
    for (int n = 0; n <= N; ++n) {
      cat[n] = fac[2*n] * invFac[n] * invFac[n + 1];
      invCat[n] = invFac[2*n] * fac[n] * fac[n + 1];
    }
    
    int bad = 0;
    for (int i = 0; i + 1 < N; i += 2) if (S[i] != S[i + 1]) ++bad;
    
    now = 1;
    fs.clear();
    fs[0] = -1;
    fs[N + 1] = -1;
    {
      int l = -1;
      int a = 0;
      for (int j = 1; 2*j - 2 < N; ++j) {
        const int b = equal(j);
        if (~b) {
          if (~a) {
            if (j - l == b - a) now *= cat[j - l + 1];
          }
          fs[j] = b;
          l = j;
          a = b;
        }
      }
    }
// cerr<<"bad = "<<bad<<", now = "<<now<<", fs = ";pv(fs.begin(),fs.end());
    
    for (; Q--; ) {
      int O;
      scanf("%d", &O);
      if (O == 1) {
        int I;
        scanf("%d", &I);
        --I;
        
        if ((I^1) < N && S[I] != S[I^1]) --bad;
        S[I] ^= 'Y' ^ 'N';
        if ((I^1) < N && S[I] != S[I^1]) ++bad;
        for (int j = (I/2 + 1) - 1; j <= (I/2 + 1) + 1; ++j) if (1 <= j && 2*j - 2 < N) update(j, equal(j));
// cerr<<"bad = "<<bad<<", now = "<<now<<", fs = ";pv(fs.begin(),fs.end());
      } else if (O == 2) {
        int K;
        scanf("%d", &K);
// cerr<<COLOR("93")<<S<<" "<<K<<COLOR()<<endl;
        Mint ans = 0;
        if (!bad) {
          auto it = fs.end(); --it; --it;
          const int j = it->first;
          const int b = it->second;
          if (2*j - 1 == N) {
            if (K == b) ans += 1;
          } else if (2*j - 1 == N - 1) {
            // no condition
            if (K == b || K == b + 1) ans += 1;
          } else {
            assert(2*j < N);
            // (2j-1, b) -> (N, K)
            const int y = K - b;
            const int x = (N - (2*j - 1)) - y;
            if (S[2*j] == 'N') {
// cerr<<COLOR("91")<<"above "<<COLOR();
              // =j, >=j+1, ...
              assert(b == j);
              // y - x > -2
              if (x >= 0 && y >= 0 && y - x > -2) {
                ans += binom(x + y, x);
                ans -= binom(x + y, y + 2);
              }
            } else {
// cerr<<COLOR("94")<<"below "<<COLOR();
              // =j-1, <=j, <=j+1, ...
              assert(b == j - 1);
              // y - x < 2
              if (x >= 0 && y >= 0 && y - x < 2) {
                ans += binom(x + y, x);
                ans -= binom(x + y, y - 2);
              }
            }
          }
// cerr<<"ans = "<<ans<<endl;
          ans *= now;
        }
        printf("%u\n", ans.x);
      } else assert(false);
    }
  }
  return 0;
}