#1191321 (C++23) No.3753 Certainly a Cretan

• 問題: No.3753 Certainly a Cretan
• ユーザー: igeee
• 提出日時: 2026-10-03 12:51:16
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 271 ms / 2,500 ms
• コード長: 6,952 bytes
• コンパイル時間: 5,306 ms
• コンパイル使用メモリ: 422,416 KB
• 実行使用メモリ: 74,772 KB
• 最終ジャッジ日時: 2026-10-03 12:51:29
• 合計ジャッジ時間: 10,742 ms
• ジャッジサーバーID （参考情報）: judge4_0 / judge3_0

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

ソースコード

#ifdef ONLINE_JUDGE
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#endif
#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define rrep(i,start,end) for (ll i = start;i >= (ll)(end);i--)
#define repn(i,end) for(ll i = 0; i <= (ll)(end); i++)
#define reps(i,start,end) for(ll i = start; i < (ll)(end); i++)
#define repsn(i,start,end) for(ll i = start; i <= (ll)(end); i++)
#define each(p,a) for(auto &p:a)
typedef vector<ll> vll;
typedef vector<pair<ll ,ll>> vpll;
typedef vector<vector<pair<ll ,ll>>> vvpll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;
typedef set<ll> sll;
typedef map<ll , ll> mpll;
typedef pair<ll ,ll> pll;
typedef tuple<ll , ll , ll> tpl3;
typedef tuple<ll , ll , ll , ll> tpl4;
typedef tuple<ll , ll , ll , ll , ll> tpl5;
typedef tuple<ll , ll , ll , ll , ll , ll> tpl6;
#define LL(...) ll __VA_ARGS__; input(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; input(__VA_ARGS__)
#define Str(...) string __VA_ARGS__; input(__VA_ARGS__)
#define Ch(...) char __VA_ARGS__; input(__VA_ARGS__)
#define all(a)  (a).begin(),(a).end()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define sz(x) (ll)x.size()
#define fr first
#define sc second
// << std::fixed << std::setprecision(10)
const ll INF = 1LL << 60;
const ld EPS = 1e-9;
 
ll lceil(ll a,ll b){if(a%b==0){return a/b;}if(a>=0){return (a/b)+1;}else{return -((-a)/b);}}
ll lfloor(ll a,ll b){if(a%b==0){return a/b;}if(a>=0){return (a/b);}else{return -((-a)/b)-1;}}
inline ll positive_mod(ll a,ll m){return (a % m + m)%m;}
inline ll popcnt(ull a){ return __builtin_popcountll(a);}
//0indexed
inline ll topbit(ll a){assert(a != 0);return 63 - __builtin_clzll(a);}
inline ll smlbit(ll a){assert(a != 0);return __builtin_ctzll(a);}
template<class T> bool chmin(T& a, T b){if(a > b){a = b;return true;}return false;}
template<class T> bool chmax(T& a, T b){if(a < b){a = b;return true;}return false;}
template<typename T> std::istream &operator>>(std::istream&is,std::vector<T>&v){for(T &in:v){is>>in;}return is;}
template<typename T> std::ostream &operator<<(std::ostream&os,const std::vector<T>&v){for(auto it=std::begin(v);it!=std::end(v);){os<<*it<<((++it)!=std::end(v)?" ":"");}return os;}
template<typename T1, typename T2>std::ostream &operator<< (std::ostream &os, std::pair<T1,T2> p){os << "{" << p.first << "," << p.second << "}";return os;}
template<class... T>void input(T&... a){(cin >> ... >> a);}
void print(){cout << endl;}
template<class T, class... Ts>void print(const T& a, const Ts&... b){cout << a;((cout << ' ' << b), ...);cout << endl;}
template<class T> void pspace(const T& a){ cout << a << ' ';}
void perr(){cerr << endl;}
template<class T, class... Ts>void perr(const T& a, const Ts&... b){cerr << a;((cerr << ' ' << b), ...);cerr << endl;}
void yes(bool i = true){ return print(i?"yes":"no"); }
void Yes(bool i = true){ return print(i?"Yes":"No"); }
void YES(bool i = true){ return print(i?"YES":"NO"); }
template <class T> vector<T> &operator++(vector<T> &v) {for(auto &e : v) e++;return v;}
template <class T> vector<T> operator++(vector<T> &v, signed) {auto res = v;for(auto &e : v) e++;return res;}
template <class T> vector<T> &operator--(vector<T> &v) {for(auto &e : v) e--;return v;}
template <class T> vector<T> operator--(vector<T> &v, signed) {auto res = v;for(auto &e : v) e--;return res;}
//grid探索用
vector<ll> _ta = {0,0,1,-1,1,1,-1,-1};
vector<ll> _yo = {1,-1,0,0,1,-1,1,-1};
bool isin(ll now_i,ll now_j,ll h,ll w){return (0<=now_i && now_i < h && 0 <= now_j && now_j < w);}
  
ll lpow(ll x,ll n){ll ans = 1;while(n >0){if(n & 1)ans *= x;x *= x;n >>= 1;}return ans;}
ll Modlpow(ll x,ll n,ll m){ll ans = 1;ll a = x%m;while(n >0){if(n & 1){ans *= a;ans%= m;}a *= a;a %= m;n >>= 1;}return ans;} 
const ll MOD9 = 998244353LL;
const ll MOD10 = 1000000007LL;


using mint = modint998244353;

//最強,前処理(n), 計算(1)
//n,k <= 10^7の時
const ll MOD = 998244353;
vector<long long> fact, fact_inv, inv;
/*  init_nCk :二項係数のための前処理
    計算量:O(n)
*/
void init_nCk(ll SIZE) {
    fact.resize(SIZE + 5);
    fact_inv.resize(SIZE + 5);
    inv.resize(SIZE + 5);
    fact[0] = fact[1] = 1;
    fact_inv[0] = fact_inv[1] = 1;
    inv[1] = 1;
    for (int i = 2; i < SIZE + 5; i++) {
        fact[i] = fact[i - 1] * i % MOD;
        inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;//iの逆元
        fact_inv[i] = fact_inv[i - 1] * inv[i] % MOD;//i!の逆元
    }
}
/*  nCk :MODでの二項係数を求める(前処理 int_nCk が必要)
    計算量:O(1)
*/
long long nCk(ll n, ll k) {
    if(n < k || (n < 0 || k < 0))return 0;
    return fact[n] * (fact_inv[k] * fact_inv[n - k] % MOD) % MOD;
}

int main(){
  ios::sync_with_stdio(false);cin.tie(nullptr);
  init_nCk(lpow(10,6)*2);
  LL(n,q);
  Str(s);
  set<ll> se;
  mint ans = 1;
  ll ki = 0;
  se.insert(0);

  auto cat = [&](ll m){//合計移動数m個(偶数のカタラン数)
    mint ret = nCk(m,m/2);
    ret /= m/2 + 1;
    return ret;
  };

  reps(i,1,n){
    if(s[i] != s[i-1]){
      if(i %2 == 1)ki++;
      if(i%2==0 && *se.rbegin()%2==0){
        ans *= cat(i-*se.rbegin());
      }
      se.insert(i);
    }
  }
  auto add = [&](ll i){
    //iを入れる
    if(i == n)return ;
    assert(!se.contains(i));
    auto it = se.lower_bound(i);
    auto pit = prev(it);
    se.insert(i);
    if(it != se.end()){
      if(*it %2==0  && *pit%2==0){
        //引く
        ans /= cat(*it-*pit);
      }
    }
    if(i % 2 == 1){
      ki++;
      return ;
    }
    if(*pit %2==0){
      ans *= cat(i-*pit);
    }
    if(it != se.end() && *it %2 == 0){
      ans *= cat(*it-i);
    }
  };
  auto erase = [&](ll i){
    if(i == 0)return;
    assert(se.contains(i));
    se.erase(i);
    auto nit = se.lower_bound(i);
    auto pit =prev(nit);
    if(i % 2 == 1)ki--;
    else{
      if(*pit%2==0)ans /= cat(i-*pit);
      if(nit != se.end() &&*nit%2==0){
        ans /= cat(*nit-i);
      }
    }
    
    if(nit != se.end() && *nit%2==0&&*pit%2==0){
      ans *= cat(*nit-*pit);
    }
  };

  while(q--){
    LL(type);
    if(type ==1){
      LL(i);
      i--;
      if(!se.contains(i))add(i);
      else erase(i);
      if(!se.contains(i+1))add(i+1);
      else erase(i+1);
      s[i] = s[i] == 'Y' ? 'N' : 'Y';
      //
    }else{
      LL(K);
      ll b = *se.rbegin();
      ll rem = n-b;
      b /= 2;
      if(K-b < 0 || K-b > rem || ki > 0 ){
        cout << 0 << endl;
        continue;
      }
      K-=b;
      mint ret = ans;
      // rem にK人Lがいる
      if(s.back() == 'Y'){
        if(K*2 > rem)ret = 0;
        ret *= nCk(rem,K) - nCk(rem,(K)-1);
      }else{
        if(2*(rem-K) > rem)ret = 0;
        ret *= nCk(rem,K) - nCk(rem,(rem-K)-1);
      }
      cout << ret.val() << endl;
    }
  }
}