#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; constexpr int FACT_SIZE = 1000000; mint Fact[FACT_SIZE + 1]; mint iFact[FACT_SIZE + 1]; const auto fact_init = [] { Fact[0] = mint::raw(1); for(int i = 1; i <= FACT_SIZE; ++i) { Fact[i] = Fact[i-1] * i; } iFact[FACT_SIZE] = Fact[FACT_SIZE].inv(); for(int i = FACT_SIZE; i; --i) { iFact[i-1] = iFact[i] * i; } return false; }(); mint comb(int n, int k) { if (k == 0) return mint::raw(1); assert(n >= 0 && k >= 0); if (k > n) return mint::raw(0); return Fact[n] * iFact[n - k] * iFact[k]; } mint icomb(int n, int k) { return iFact[n] * Fact[n - k] * Fact[k]; } mint fact(int n) {return Fact[n];} mint perm(int n, int k) { assert(0 <= n); return Fact[n] * iFact[n - k]; } vector fps_inverse(vector f, int precision) { int n = f.size(); assert(n >= 1 && f[0] != 0); int len = 1; const int z = (int)std::bit_ceil((unsigned int)(precision)); vector g{f[0].inv()}; const mint inv4 = mint(4).inv(); mint inv4k = 1; while (len < z) { int nlen = 2 * len; vector ft(f.begin(), f.begin() + min(n, nlen)); ft.resize(nlen); internal::butterfly(ft); vector gt = g; gt.resize(nlen); internal::butterfly(gt); for (int i = 0; i < nlen; i++) ft[i] *= gt[i]; internal::butterfly_inv(ft); ft.erase(ft.begin(), ft.begin() + len); ft.resize(nlen); internal::butterfly(ft); for (int i = 0; i < nlen; i++) ft[i] *= gt[i]; internal::butterfly_inv(ft); inv4k *= inv4; mint c = -inv4k; for (int i = 0; i < len; i++) g.emplace_back(c * ft[i]); len = nlen; } g.resize(precision); return g; } vector kth_power_sums(mint n, int m) { // e^0+e^x+e^2x+...+e^(n-1)x // = ((e^nx-1)/x) / ((e^x-1)/x) // =: f / g // init_fact(m + 1); vector f(m), g(m); mint pow_n = n; for (int i = 0; i < m; i++) { f[i] = pow_n * iFact[i + 1]; g[i] = iFact[i + 1]; pow_n *= n; } vector res = convolution(f, fps_inverse(g, m)); res.resize(m); for (int i = 0; i < m; i++) res[i] *= Fact[i]; return res; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int h, w, n, k; cin >> h >> w >> n >> k; int ubh = -1, ubw = -1; mint mxh = -1, mxw = -1; mint lh = -1, lw = -1; rep(_, 2) { if (h >= 2 * k) { ubh = k; mxh = k; lh = h - 2 * k + 2; } else { ubh = h - k + 1; mxh = h - k + 1; lh = 2 * k - h; } swap(h, w); swap(ubh, ubw); swap(mxh, mxw); swap(lh, lw); } mint tot = mint(h - k + 1) * (w - k + 1); auto ph = kth_power_sums(ubh, n + 1); auto pw = kth_power_sums(ubw, n + 1); ph[0]--; pw[0]--; mint ans; rep(i, n + 1) { mint coeff = comb(n, i) * tot.pow(n - i); if (i % 2) coeff *= -1; mint v; v += (mxh * mxw).pow(i) * lh * lw; v += mxh.pow(i) * lh * pw[i] * 2; v += ph[i] * mxw.pow(i) * lw * 2; v += ph[i] * pw[i] * 4; ans += coeff * v; } ans /= tot.pow(n); ans = mint(h) * w - ans; cout << ans.val() << '\n'; }