#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const vector &as); template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &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 void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #define COLOR(s) ("\x1b[" s "m") //////////////////////////////////////////////////////////////////////////////// template 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(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(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(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(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 friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template 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; 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 cat, invCat; Mint now; map 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 = "<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<=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<= 0 && y >= 0 && y - x < 2) { ans += binom(x + y, x); ans -= binom(x + y, y - 2); } } } // cerr<<"ans = "<