#if __INCLUDE_LEVEL__ == 0 #include using namespace std; #include __BASE_FILE__ namespace { Comb comb(1e6); void solve() { int h, w, n, k; cin >> tie(h, w, n, k); vector pw(n + 1, 1); for (int i : rep(n)) { pw[i + 1] = pw[i] * (h - k + 1) * (w - k + 1); } int mh = min(k, h - k + 1); int mw = min(k, w - k + 1); int lh = abs(h - k * 2 + 1) + 1; int lw = abs(w - k * 2 + 1) + 1; vector denom(n + 1); for (int i : rep1(0, n)) { denom[i] = comb.recip_fact(i + 1); } denom = inv(denom); vector sh(n + 1); for (int i : rep1(0, n)) { sh[i] = (Fp(mh).pow(i + 1) - 1) * comb.recip_fact(i + 1); } sh *= denom; for (int i : rep1(0, n)) { sh[i] *= comb.fact(i); } vector sw(n + 1); for (int i : rep1(0, n)) { sw[i] = (Fp(mw).pow(i + 1) - 1) * comb.recip_fact(i + 1); } sw *= denom; for (int i : rep1(0, n)) { sw[i] *= comb.fact(i); } Fp ans = 0; for (int i : rep1(0, n)) { ans += comb.binom(n, i) * pw[i] * Fp(-1).pow(n - i) * sh[n - i] * sw[n - i]; } ans *= 4; for (int i : rep1(0, n)) { ans += comb.binom(n, i) * pw[i] * Fp(-mw).pow(n - i) * sh[n - i] * lw * 2; } for (int i : rep1(0, n)) { ans += comb.binom(n, i) * pw[i] * Fp(-mh).pow(n - i) * sw[n - i] * lh * 2; } ans += (pw[1] - Fp(mh) * mw).pow(n) * lh * lw; ans /= pw[n]; ans = Fp(h) * w - ans; print(ans); } } // namespace int main() { ios::sync_with_stdio(false); cin.tie(nullptr); solve(); } #else // __INCLUDE_LEVEL__ #undef assert #define assert(expr) (expr) || (__builtin_unreachable(), 0) #include template vector make_vector_for_overwrite(int n) { static_assert(is_trivially_destructible_v); vector v; v.reserve(n); auto p = (T**)&v; p[1] = p[2]; return v; } template class Comb { public: Comb() = default; explicit Comb(int max_n) : fact_(make_vector_for_overwrite(max_n + 1)), recip_fact_(make_vector_for_overwrite(max_n + 1)) { fact_[0] = 1; for (int n = 1; n <= max_n; ++n) { fact_[n] = fact_[n - 1] * n; } recip_fact_[max_n] = 1 / fact_[max_n]; for (int n = max_n; 1 <= n; --n) { recip_fact_[n - 1] = n * recip_fact_[n]; } } T recip(int n) const { assert(n); return n < 0 ? -recip(-n) : recip_fact_[n] * fact_[n - 1]; } T fact(int n) const { assert(0 <= n); return fact_[n]; } T recip_fact(int n) const { return n < 0 ? 0 : recip_fact_[n]; } T falling_fact(int n, int k) const { assert(0 <= n || n < k); if (n < 0) { T t = falling_fact(k - n - 1, k); return k & 1 ? -t : t; } return n < k ? 0 : recip_fact(n - k) * fact(n); } T recip_falling_fact(int n, int k) const { assert(n < 0 || k <= n); return falling_fact(n - k, -k); } T rising_fact(int n, int k) const { assert(n <= 0 || 0 < n + k); return falling_fact(n + k - 1, k); } T recip_rising_fact(int n, int k) const { assert(0 < n || n + k <= 0); return falling_fact(n - 1, -k); } T binom(int n, int k) const { if ((n < 0) ^ (k < 0) ^ (n < k)) { return 0; } if (n < 0 && k < 0) { k = n - k; } return recip_fact(k) * falling_fact(n, k); } T recip_binom(int n, int k) const { assert((0 <= n) ^ (0 <= k) ^ (k <= n)); k = max(k, n - k); return recip_falling_fact(n, k) * fact(k); } T multiset(int n, int k) const { return binom(n + k - 1, k); } T recip_multiset(int n, int k) const { assert((0 < n) ^ (0 <= k) ^ (0 < n + k)); return recip_binom(n + k - 1, k); } private: vector fact_; vector recip_fact_; }; template bool chmin(T& x, U&& y) { return y < x && (x = forward(y), true); } template bool chmax(T& x, U&& y) { return x < y && (x = forward(y), true); } namespace std { template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } template istream& operator>>(istream& is, tuple& t) { return apply([&is](auto&... xs) -> istream& { return (is >> ... >> xs); }, t); } template istream& operator>>(istream& is, tuple&& t) { return is >> t; } template >* = nullptr> auto operator>>(istream& is, R&& r) -> decltype(is >> *begin(r)) { for (auto&& e : r) { is >> e; } return is; } template ostream& operator<<(ostream& os, const pair& p) { return os << p.first << ' ' << p.second; } template ostream& operator<<(ostream& os, const tuple& t) { auto f = [&os](const auto&... xs) -> ostream& { [[maybe_unused]] auto sep = ""; ((os << exchange(sep, " ") << xs), ...); return os; }; return apply(f, t); } template >* = nullptr> auto operator<<(ostream& os, R&& r) -> decltype(os << *begin(r)) { auto sep = ""; for (auto&& e : r) { os << exchange(sep, " ") << e; } return os; } } // namespace std namespace atcoder { template * = nullptr> istream& operator>>(istream& is, T& x) { int v; is >> v; x = T::raw(v); return is; } template * = nullptr> ostream& operator<<(ostream& os, const T& x) { return os << x.val(); } } // namespace atcoder template void print(Ts&&... xs) { cout << tie(xs...) << '\n'; } inline auto rep(int l, int r) { return views::iota(min(l, r), r); } inline auto rep(int n) { return rep(0, n); } inline auto rep1(int l, int r) { return rep(l, r + 1); } inline auto rep1(int n) { return rep(1, n + 1); } inline auto per(int l, int r) { return rep(l, r) | views::reverse; } inline auto per(int n) { return per(0, n); } inline auto per1(int l, int r) { return per(l, r + 1); } inline auto per1(int n) { return per(1, n + 1); } using Fp = atcoder::modint998244353; using Fps = std::vector; int sz(const Fps& a) { return a.size(); } Fps operator-(Fps a) { for (auto&& e : a) e = -e; return a; } Fps& operator+=(Fps& a, const Fps& b) { if (sz(a) < sz(b)) a.reserve(sz(b)), a.resize(sz(b)); for (int i = 0; i < sz(b); ++i) a[i] += b[i]; return a; } Fps operator+(Fps a, const Fps& b) { return std::move(a += b); } Fps& operator-=(Fps& a, const Fps& b) { if (sz(a) < sz(b)) a.reserve(sz(b)), a.resize(sz(b)); for (int i = 0; i < sz(b); ++i) a[i] -= b[i]; return a; } Fps operator-(Fps a, const Fps& b) { return std::move(a -= b); } Fps& operator*=(Fps& a, Fp b) { for (auto&& e : a) e *= b; return a; } Fps operator*(Fps a, Fp b) { return std::move(a *= b); } Fps operator*(Fp a, Fps b) { return std::move(b *= a); } Fps& operator/=(Fps& a, Fp b) { b = b.inv(); for (auto&& e : a) e *= b; return a; } Fps operator/(Fps a, Fp b) { return std::move(a /= b); } Fps fft(const Fps& a, int n) { Fps res(n); std::copy(a.begin(), a.begin() + std::min(n, sz(a)), res.begin()); atcoder::internal::butterfly(res); return res; } Fps circ(Fps&& a, const Fps& b) { if (sz(a) < sz(b)) a.reserve(sz(b)), a.resize(sz(b)); for (int i = 0; i < sz(b); ++i) a[i] *= b[i]; return a; } Fps circ(Fps&& a) { for (auto&& e : a) e *= e; return a; } Fps ifft(Fps&& a, int size) { int n = sz(a); atcoder::internal::butterfly_inv(a); a.resize(size); a *= (1 - Fp::mod()) / n; return a; } Fps operator*(const Fps& a, const Fps& b) { if (a.empty() || b.empty()) return {}; if (std::min(sz(a), sz(b)) <= 60) { Fps res(std::max(sz(a), sz(b))); for (int i = 0; i < sz(a); ++i) for (int j = 0; j < sz(b); ++j) { if (i + j == sz(res)) break; res[i + j] += a[i] * b[j]; } return res; } int n = __bit_ceil(sz(a) + sz(b) - 1); auto buf = fft(a, n); if (&a == &b) buf = circ(std::move(buf)); else buf = circ(std::move(buf), fft(b, n)); return ifft(std::move(buf), std::max(sz(a), sz(b))); } Fps& operator*=(Fps& a, const Fps& b) { return a = a * b; } Fps inv(const Fps& a) { Fps res{a[0].inv()}; for (int n = 1; n < sz(a); n *= 2) { auto f_res = fft(res, 2 * n); Fps buf = ifft(circ(fft(a, 2 * n), f_res), 2 * n); std::fill(buf.begin(), buf.begin() + n, 0); buf = ifft(circ(fft(buf, 2 * n), f_res), std::min(2 * n, sz(a))); for (int i = n; i < sz(buf); ++i) res.push_back(-buf[i]); } return res; } Fps deriv(const Fps& a) { Fps res(sz(a)); for (int i = 1; i < sz(a); ++i) res[i - 1] = a[i] * i; return res; } Fps integ(const Fps& a) { Fps res(sz(a)); for (int i = 1; i < sz(res); ++i) res[i] = a[i - 1] / i; return res; } Fps log(const Fps& a) { return integ(deriv(a) * inv(a)); } Fps exp(const Fps& a) { Fps res{1}; for (res.reserve(sz(a)); sz(res) < sz(a);) { res.resize(std::min(2 * sz(res), sz(a))); res *= Fps{1} - log(res) + Fps(a.begin(), a.begin() + sz(res)); } return res; } #endif // __INCLUDE_LEVEL__