#include #include using namespace std; using namespace atcoder; // using mint = modint1000000007; // const int mod = 1000000007; using mint = modint998244353; const int mod = 998244353; const int INF = 1e9; // const long long LINF = 1e18; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i, l, r) for (int i = (l); i < (r); ++i) #define rrep(i, n) for (int i = (n)-1; i >= 0; --i) #define rrep2(i, l, r) for (int i = (r)-1; i >= (l); --i) #define all(x) (x).begin(), (x).end() #define allR(x) (x).rbegin(), (x).rend() #define P pair template inline bool chmax(A& a, const B& b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A& a, const B& b) { if (a > b) { a = b; return true; } return false; } #ifndef KWM_T_MATH_MODINT_BINOM_HPP #define KWM_T_MATH_MODINT_BINOM_HPP #include #include namespace kwm_t::math::modint { /** * @brief 二項係数・順列・多項係数(modint用) * * 典型用途: * nCk, nPk, 多項係数 * * 計算量: * 前計算 O(N) * クエリ O(1) * * @tparam Mint modint型 (例: atcoder::static_modint) * * 制約 / 注意: * - mod は素数 * - n < mod(階乗が0にならない範囲) * * 使用例: * Binom C(2000000); * C.com(n, k); * * verified: */ template struct Binom { std::vector fact, ifact; Binom(int n = 2000006) { init(n); } void init(int n) { fact.resize(n + 1); ifact.resize(n + 1); fact[0] = 1; for (int i = 1; i <= n; ++i) { fact[i] = fact[i - 1] * i; } ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) { ifact[i - 1] = ifact[i] * i; } } // nCk Mint com(int n, int k) const { if (k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n - k]; } Mint operator()(int n, int k) const { return com(n, k); } // nPk Mint perm(int n, int k) const { if (k < 0 || k > n) return 0; return fact[n] * ifact[n - k]; } // nCk (nが大きくkが小さい場合) Mint com_sub(long long n, long long k) const { if (k < 0 || k > n) return 0; if (n - k < k) k = n - k; assert(k < (int)fact.size()); Mint res = ifact[k]; for (long long i = 0; i < k; ++i) { res *= (n - i); } return res; } // 多項係数 template Mint multinomial(int n, const Ints&... ms) const { Mint res = fact[n]; int sum = 0; for (int m : {ms...}) { if (m < 0 || m > n) return 0; res *= ifact[m]; sum += m; } if (sum > n) return 0; res *= ifact[n - sum]; return res; } // 1/x Mint inv(int x) const { if (x < (int)fact.size()) { return fact[x - 1] * ifact[x]; } return Mint(x).inv(); } // nCk の逆数 Mint inv_com(int n, int k) const { if (k < 0 || k > n) return 0; return ifact[n] * fact[k] * fact[n - k]; } }; } // namespace kwm_t::math::modint #endif // KWM_T_MATH_MODINT_BINOM_HPP #ifndef KWM_T_ALGORITHM_RUN_LENGTH_ENCODING_HPP #define KWM_T_ALGORITHM_RUN_LENGTH_ENCODING_HPP #include #include #include namespace kwm_t::algorithm { /** * @brief Run Length Encoding(連長圧縮) * * 任意の forward iterator に対して適用可能 * * 計算量: * O(N) * * 制約: * - 要素型に == が定義されていること * verified * https://atcoder.jp/contests/abc452/submissions/74695137 * https://atcoder.jp/contests/awc0051/submissions/75170743 */ template std::vector::value_type, int>> run_length_encoding(It first, It last) { using T = typename std::iterator_traits::value_type; std::vector> ret; if (first == last) return ret; It it = first; while (it != last) { It jt = it; int cnt = 0; while (jt != last && *jt == *it) { ++jt; ++cnt; } ret.emplace_back(*it, cnt); it = jt; } return ret; } // コンテナ版 template std::vector> run_length_encoding(const Container& c) { return run_length_encoding(c.begin(), c.end()); } } // namespace kwm_t::algorithm #endif // KWM_T_ALGORITHM_RUN_LENGTH_ENCODING_HPP #ifndef KWM_T_DATA_STRUCTURE_INTERVAL_SET_HPP #define KWM_T_DATA_STRUCTURE_INTERVAL_SET_HPP #include #include #include /** * @brief 半開区間集合 [l, r) を管理するデータ構造 * * 典型用途: * - 区間の union 管理 * - mex 管理 * - 区間の被覆判定 * * 計算量: * - 各操作 O(log N) * * @tparam T * - 順序比較可能 * * 制約 / 注意: * - 半開区間 [l, r) * - 番兵として (-INF, -INF), (INF, INF) を内部に持つ * * verified: * - https://atcoder.jp/contests/abc430/submissions/75172066 * - https://atcoder.jp/contests/awc0078/submissions/76170297 */ namespace kwm_t::data_structure { template class IntervalSet { public: explicit IntervalSet(T limit) : TINF(limit) { ranges_.emplace(-TINF, -TINF); ranges_.emplace(TINF, TINF); } // [l,r) がカバーされているか bool isCovered(T l, T r) const noexcept { if (l >= r) return true; auto it = std::prev(ranges_.upper_bound({ l, TINF })); return (it->first <= l && r <= it->second); } bool isCovered(T x) const noexcept { return isCovered(x, x + 1); } // カバー区間取得 std::pair getCoveringRange(T l, T r) const noexcept { auto it = std::prev(ranges_.upper_bound({ l, TINF })); if (it->first <= l && r <= it->second) return *it; return { -TINF, -TINF }; } std::pair getCoveringRange(T x) const noexcept { return getCoveringRange(x, x + 1); } std::pair front() const noexcept { auto it = std::next(ranges_.begin()); return *it; } std::pair back() const noexcept { auto it = std::prev(std::prev(ranges_.end())); return *it; } // --- 挿入 --- void insertRange( T l, T r, const std::function& onInsert = [](T, T) {}, const std::function& onErase = [](T, T) {} ) { if (l >= r) return; auto it = std::prev(ranges_.upper_bound({ l, TINF })); if (isCovered(l, r)) return; // 左マージ if (it->first <= l && l <= it->second) { l = it->first; eraseRange(it, onErase); } else { ++it; } // 右方向マージ while (it->first <= r) { r = std::max(r, it->second); eraseRange(it, onErase); } addRange(l, r, onInsert); } void insertPoint( T x, const std::function& onInsert = [](T, T) {}, const std::function& onErase = [](T, T) {} ) { insertRange(x, x + 1, onInsert, onErase); } // --- 削除 --- void eraseRange( T l, T r, const std::function& onInsert = [](T, T) {}, const std::function& onErase = [](T, T) {} ) { if (l >= r) return; auto it = std::prev(ranges_.upper_bound({ l, TINF })); // 1区間内 if (it->first <= l && r <= it->second) { auto [L, R] = *it; eraseRange(it, onErase); if (L < l) addRange(L, l, onInsert); if (r < R) addRange(r, R, onInsert); return; } // 左端 if (it->first <= l && l < it->second) { auto [L, R] = *it; eraseRange(it, onErase); addRange(L, l, onInsert); } else { ++it; } // 中央 while (it->second <= r) { eraseRange(it, onErase); } // 右端 if (it->first < r && r < it->second) { auto [L, R] = *it; eraseRange(it, onErase); addRange(r, R, onInsert); } } void erasePoint( T x, const std::function& onInsert = [](T, T) {}, const std::function& onErase = [](T, T) {} ) { eraseRange(x, x + 1, onInsert, onErase); } int rangeCount() const noexcept { return (int)ranges_.size() - 2; } // mex T mex(T x = 0) const noexcept { if (!isCovered(x)) return x; auto it = std::prev(ranges_.upper_bound({ x, TINF })); return it->second; } void debug() const noexcept { for (auto [l, r] : ranges_) { if (l != -TINF && l != TINF) { std::cout << "[" << l << "," << r << ")\n"; } } } private: std::set> ranges_; T TINF; void eraseRange(typename std::set>::iterator& it, const std::function& onErase) { onErase(it->first, it->second); it = ranges_.erase(it); } void addRange(T l, T r, const std::function& onInsert) { onInsert(l, r); ranges_.emplace(l, r); } }; } // namespace kwm_t::data_structure #endif // KWM_T_DATA_STRUCTURE_INTERVAL_SET_HPP int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); kwm_t::math::modint::Binom binom; int n, q; cin >> n >> q; string s; cin >> s; auto cat = [&](int n, bool inv = false) -> mint { if (inv) return binom.ifact[2 * n] * binom.fact[n] * binom.fact[n + 1]; return binom.fact[2 * n] * binom.ifact[n] * binom.ifact[n + 1]; }; // +1:p,-1;q auto rastY = [&](int p, int q)->mint { if (p < 0 || q < 0 || p < q)return 0; return binom(p + q, p) - binom(p + q, p + 1); }; // +1:p,-1;q auto rastN = [&](int p, int q)->mint { if (p < 0 || q < 0 || p > q)return 0; return binom(p + q, q) - binom(p + q, q + 1); }; mint ans = 1;// 最終ブロックは自前で計算しろ int ngcnt = 0; { // naive auto rle = kwm_t::algorithm::run_length_encoding(s); rep(i, rle.size()) { int sz = rle[i].second; if (i != rle.size() - 1) { if (sz % 2 == 1) ngcnt++; else ans *= cat(sz / 2); } } } kwm_t::data_structure::IntervalSet stY(INF), stN(INF); rep(i, n) { if (s[i] == 'Y')stY.insertPoint(i); else stN.insertPoint(i); } auto add = [&](int l, int r) -> void { if (r == n)return; int sz = r - l; if (sz % 2 == 0) ans *= cat(sz / 2); else ngcnt++; }; auto del = [&](int l, int r) -> void { if (r == n)return; int sz = r - l; if (sz % 2 == 0) ans *= cat(sz / 2, true); else ngcnt--; }; while (q--) { int t; cin >> t; if (t == 1) { int i; cin >> i; i--; if (s[i] == 'Y') { stY.erasePoint(i, add, del); stN.insertPoint(i, add, del); s[i] = 'N'; } else { stN.erasePoint(i, add, del); stY.insertPoint(i, add, del); s[i] = 'Y'; } } else { int k; cin >> k; if (ngcnt) { cout << 0 << endl; continue; } if (s[n - 1] == 'Y') { auto [l, r] = stY.getCoveringRange(n - 1); k -= l / 2; mint val = ans * rastY(r - l - k, k); cout << val.val() << endl; } else { auto [l, r] = stN.getCoveringRange(n - 1); k -= l / 2; mint val = ans * rastN(r - l - k, k); cout << val.val() << endl; } } } return 0; }