#1191277 (C++17) No.3753 Certainly a Cretan

• 問題: No.3753 Certainly a Cretan
• ユーザー: dyktr_06
• 提出日時: 2026-10-03 02:11:52
• 言語: C++17 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 459 ms / 2,500 ms
• コード長: 16,740 bytes
• コンパイル時間: 1,389 ms
• コンパイル使用メモリ: 223,140 KB
• 実行使用メモリ: 98,148 KB
• 最終ジャッジ日時: 2026-10-03 02:12:41
• 合計ジャッジ時間: 9,264 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge4_0

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

ソースコード

#include <bits/stdc++.h>

using namespace std;

#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))

using i64 = int64_t;
using i128 = __int128_t;

using ll = long long;
using ul = unsigned long long;
using ull = unsigned long long;
using ld = long double;
using vi = vector<int>;
using vll = vector<long long>;
using vull = vector<unsigned long long>;
using vc = vector<char>;
using vst = vector<string>;
using vd = vector<double>;
using vld = vector<long double>;
using P = pair<long long, long long>;

template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); }

const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);

template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; }

template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }

template<class T, class U>
void inGraph(vector<vector<T>> &G, U n, U m, bool directed = true, bool zero_index = true){
    G.resize(n);
    for(int i = 0; i < m; i++){
        int a, b;
        cin >> a >> b;
        if(!zero_index) a--, b--;
        G[a].push_back(b);
        if(!directed) G[b].push_back(a);
    }
}

template <typename T>
long long binary_search(long long ok, long long ng, T check){
    while(abs(ok - ng) > 1){
        long long mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

template <typename T>
long double binary_search_real(long double ok, long double ng, T check, int iter = 100){
    for(int i = 0; i < iter; ++i){
        long double mid = (ok + ng) / 2;
        if(check(mid)) ok = mid;
        else ng = mid;
    }
    return ok;
}

long long trisum(long long a, long long b){
    if(a > b) return 0;
    long long res = ((b - a + 1) * (a + b)) / 2;
    return res;
}

template <typename T>
T intpow(T x, int n){
    T ret = 1;
    while(n > 0) {
        if(n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}

template <typename T>
T getDivision(T a, T b){
    if(b == 0) return -1;
    if(a >= 0 && b > 0){
        return a / b;
    } else if(a < 0 && b > 0){
        return a / b - (a % b != 0);
    } else if(a >= 0 && b < 0){
        return a / b;
    } else{
        return a / b + (a % b != 0);
    }
}

template <typename T>
T getReminder(T a, T b){
    if(b == 0) return -1;
    if(a >= 0 && b > 0){
        return a % b;
    } else if(a < 0 && b > 0){
        return ((a % b) + b) % b;
    } else if(a >= 0 && b < 0){
        return a % b;
    } else{
        return (abs(b) - abs(a % b)) % b;
    }
}

template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; ((cout << ' ' << b), ...); cout << '\n'; }
void fout(){ cout << endl; }
template<class T, class... Ts> void fout(const T &a, const Ts&... b){ cout << a; ((cout << ' ' << b), ...); cout << endl; }
void debug(){ cerr << '\n'; }
template<class T, class... Ts> void debug(const T &a, const Ts&... b){ cerr << a; ((cout << ' ' << b), ...); cerr << '\n'; }

template <typename T, T (*op)(T, T), T(*e)()>
struct SegTree{
    int _n, n;
    std::vector<T> dat;

    SegTree(int _n) : _n(_n) {
        int x = 1;
        while(_n > x){
            x *= 2;
        }
        n = x;
        dat.resize(n * 2);
        for(int i = 0; i < n * 2; ++i){
            dat[i] = e();
        }
    }
    SegTree(std::vector<T> &v) : _n((int) v.size()) {
        int x = 1;
        while((int) v.size() > x){
            x *= 2;
        }
        n = x;
        dat.resize(n * 2);
        for(int i = 0; i < n; ++i){
            set(i, (i < (int) v.size() ? v[i] : e()));
        }
        build();
    }

private:
    void set(int i, const T &x){ dat[i + n] = x; }

    void build(){
        for(int k = n - 1; k >= 1; k--) dat[k] = op(dat[k * 2], dat[k * 2 + 1]);
    }

public:
    T get(int i) const {
        assert(0 <= i && i < n);
        return dat[i + n];
    }

    void update(int i, const T &x){
        assert(0 <= i && i < n);
        i += n;
        dat[i] = x;
        while(i > 0){
            i >>= 1;  // parent
            dat[i] = op(dat[i * 2], dat[i * 2 + 1]);
        }
    }

    T query(int a, int b){
        assert(0 <= a && a <= b && b <= n);
        T vl = e();
        T vr = e();
        int l = a + n;
        int r = b + n;
        while(l < r){
            if(l & 1) vl = op(vl, dat[l++]);
            if(r & 1) vr = op(dat[--r], vr);
            l >>= 1;
            r >>= 1;
        }
        return op(vl, vr);
    }

    template <class F>
    int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if(l == _n) return _n;
        l += n;
        T sm = e();
        do{
            while(l % 2 == 0) l >>= 1;
            if(!f(op(sm, dat[l]))){
                while(l < n){
                    l = (2 * l);
                    if(f(op(sm, dat[l]))){
                        sm = op(sm, dat[l]);
                        l++;
                    }
                }
                return l - n;
            }
            sm = op(sm, dat[l]);
            l++;
        }while((l & -l) != l);
        return _n;
    }

    template <class F>
    int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if(r == 0) return 0;
        r += n;
        T sm = e();
        do{
            r--;
            while(r > 1 && (r % 2)) r >>= 1;
            if(!f(op(dat[r], sm))){
                while(r < n){
                    r = (2 * r + 1);
                    if(f(op(dat[r], sm))){
                        sm = op(dat[r], sm);
                        r--;
                    }
                }
                return r + 1 - n;
            }
            sm = op(dat[r], sm);
        }while((r & -r) != r);
        return 0;
    }
};

template <long long Modulus>
struct ModInt{
    long long val;
    static constexpr int mod() { return Modulus; }
    constexpr ModInt(const long long _val = 0) noexcept : val(_val) {
        normalize();
    }
    void normalize(){
        val = (val % Modulus + Modulus) % Modulus;
    }
    inline ModInt &operator+=(const ModInt &rhs) noexcept {
        if(val += rhs.val, val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt &operator-=(const ModInt &rhs) noexcept {
        if(val -= rhs.val, val < 0) val += Modulus;
        return *this;
    }
    inline ModInt &operator*=(const ModInt &rhs) noexcept {
        val = val * rhs.val % Modulus;
        return *this;
    }
    inline ModInt &operator/=(const ModInt &rhs) noexcept {
        val = val * inv(rhs.val).val % Modulus;
        return *this;
    }
    inline ModInt &operator++() noexcept {
        if(++val >= Modulus) val -= Modulus;
        return *this;
    }
    inline ModInt operator++(int) noexcept {
        ModInt t = val;
        if(++val >= Modulus) val -= Modulus;
        return t;
    }
    inline ModInt &operator--() noexcept {
        if(--val < 0) val += Modulus;
        return *this;
    }
    inline ModInt operator--(int) noexcept {
        ModInt t = val;
        if(--val < 0) val += Modulus;
        return t;
    }
    inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
    inline ModInt inv(void) const { return inv(val); }
    ModInt pow(long long n) const {
        assert(0 <= n);
        ModInt x = *this, r = 1;
        while(n){
            if(n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    ModInt inv(const long long n) const {
        long long a = n, b = Modulus, u = 1, v = 0;
        while(b){
            long long t = a / b;
            a -= t * b; std::swap(a, b);
            u -= t * v; std::swap(u, v);
        }
        u %= Modulus;
        if(u < 0) u += Modulus;
        return u;
    }
    friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
    friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
    friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
    friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
    friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
    friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
    friend inline std::istream &operator>>(std::istream &is, ModInt &x) noexcept {
        is >> x.val;
        x.normalize();
        return is;
    }
    friend inline std::ostream &operator<<(std::ostream &os, const ModInt &x) noexcept { return os << x.val; }
};

using mint = ModInt<MOD>;

template <typename T>
struct Combination{
    std::vector<T> memo, memoinv, inv;
    Combination() : memo(2, T(1)), memoinv(2, T(1)), inv(2, T(1)){}

    void init(const int N){
        if((int) memo.size() >= N + 1){
            return;
        }
        int prev_len = memo.size();
        memo.resize(N + 1);
        memoinv.resize(N + 1);
        inv.resize(N + 1);

        T m = -1;
        long long mod = (m.val + 1LL);
        for(int i = prev_len; i <= N; ++i){
            memo[i] = memo[i - 1] * i;
            inv[i] = mod - inv[mod % i] * (mod / i);
            memoinv[i] = memoinv[i - 1] * inv[i];
        }
    }

    inline T fact(const int n) {
        init(n);
        return memo[n];
    }
    inline T factinv(const int n) {
        init(n);
        return memoinv[n];
    }
    inline T ncr(const int n, const int r) {
        if(n < r || r < 0) return 0;
        init(n);
        return (memo[n] * memoinv[r]) * memoinv[n - r];
    }
    inline T npr(const int n, const int r) {
        if(n < r || r < 0) return 0;
        init(n);
        return memo[n] * memoinv[n - r];
    }
    // 重複組み合わせ
    inline T nhr(const int n, const int r) {
        if(n == 0 && r == 0) return 1;
        return ncr(n + r - 1, r);
    }
    // ボールの数、一個以上必要な箱の数、制限がない箱の数 (箱区別あり)
    // a = 0 の場合は重複組み合わせ
    inline T choose(const int n, const int a, const int b = 0) {
        if(n == 0) return !a;
        return ncr(n + b - 1, a + b - 1);
    }
    // +1 n 個, -1 m 個, 累積和 >= 0
    inline T cataran(const int n, const int m) {
        return cataran(n, m, 1);
    }
    // +1 n 個, -1 m 個, 累積和 > -k
    inline T cataran(const int n, const int m, const int k) {
        if(m < k) return ncr(n + m, n);
        if(m < n + k) return ncr(n + m, n) - ncr(n + m, m - k);
        return 0;
    }
    // +1 n 個, -1 m 個, 累積和 < +k
    inline T cataran2(const int n, const int m, const int k) {
        return cataran(m, n, k);
    }
};

Combination<mint> comb;

struct S{
    char l, r;
    ll cntl, cntr;
    mint s;
};

mint f(ll x){
    if(x % 2) return mint(0);
    return comb.cataran(x / 2, x / 2);
}

S op(S l, S r){
    if(l.cntl == 0 && l.cntr == 0){
        return r;
    }
    if(r.cntl == 0 && r.cntr == 0){
        return l;
    }

    if(l.cntr == 0 && r.cntr == 0){
        if(l.l == r.l){
            return {l.l, '.', l.cntl + r.cntl, 0, l.s * r.s};
        }else{
            return {l.l, r.l, l.cntl, r.cntl, l.s * r.s};
        }
    }else if(r.cntr == 0){
        if(l.r == r.l){
            return {l.l, r.l, l.cntl, l.cntr + r.cntl, l.s * r.s};
        }else{
            return {l.l, r.l, l.cntl, r.cntl, l.s * r.s * f(l.cntr)};
        }
    }else if(l.cntr == 0){
        if(l.l == r.l){
            return {l.l, r.r, l.cntl + r.cntl, r.cntr, l.s * r.s};
        }else{
            return {l.l, r.r, l.cntl, r.cntr, l.s * r.s * f(r.cntl)};
        }
    }else{
        if(l.r == r.l){
            return {l.l, r.r, l.cntl, r.cntr, l.s * r.s * f(l.cntr + r.cntl)};
        }else{
            return {l.l, r.r, l.cntl, r.cntr, l.s * r.s * f(l.cntr) * f(r.cntl)};
        }
    }
}

S e(){
    return {'Y', 'Y', 0, 0, 1};
}

ll T;

void input(){
    in(T);
}

void solve(){
    // カタラン数の練習？
    ll n, q; in(n, q);
    string s; in(s);
    SegTree<S, op, e> seg(n);
    rep(i, n){
        if(s[i] == 'Y'){
            seg.update(i, {'Y', '.', 1, 0, 1});
        }else{
            seg.update(i, {'N', '.', 1, 0, 1});
        }
    }
    while(q--){
        ll t; in(t);
        if(t == 1){
            ll i; in(i);
            i--;
            if(s[i] == 'Y') s[i] = 'N';
            else s[i] = 'Y';
            if(s[i] == 'Y'){
                seg.update(i, {'Y', '.', 1, 0, 1});
            }else{
                seg.update(i, {'N', '.', 1, 0, 1});
            }
        }else{
            ll k; in(k);
            S res = seg.query(0, n);
            mint ans = res.s;
            // debug(res.l, res.r, res.cntl, res.cntr, res.s);
            if(res.cntr == 0){
                if(res.l == 'N'){
                    ans *= comb.cataran(k, res.cntl - k);
                }else{
                    ans *= comb.cataran(res.cntl - k, k);
                }
            }else{
                ans *= f(res.cntl);
                ll cnt = (n - res.cntr) / 2;
                if(k < cnt){
                    out(0);
                    continue;
                }
                ll nk = k - cnt;
                // debug(nk, res.cntr - nk, comb.cataran(nk, res.cntr - nk));
                if(res.r == 'N'){
                    ans *= comb.cataran(nk, res.cntr - nk);
                }else{
                    ans *= comb.cataran(res.cntr - nk, nk);
                }
            }
            out(ans);
        }
    }
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(20);

    T = 1;
    // input();
    while(T--) solve();
}