#include #include using namespace std; using namespace atcoder; istream &operator>>(istream &is, modint &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint &a) { return os << a.val(); } istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); } istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; } ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } typedef long long ll; typedef vector> Graph; typedef pair pii; typedef pair pll; #define rep(i,n) for (int i = 0;i < (int)(n); i++) #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define my_sort(x) sort(x.begin(), x.end()) #define my_max(x) *max_element(all(x)) #define my_min(x) *min_element(all(x)) template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } const int INF = (1<<30) - 1; const ll LINF = (1LL<<62) - 1; const int MOD = 998244353; const int MOD2 = 1e9+7; const double PI = acos(-1); vector di = {1,0,-1,0}; vector dj = {0,1,0,-1}; #ifdef LOCAL # include # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using mint = modint998244353; int main(){ cin.tie(0); ios_base::sync_with_stdio(false); int H,W,N,K; cin >> H >> W >> N >> K; if (H > W) swap(H, W); mint ans = mint(H) * mint(W); if (H < 2 * K && W < 2 * K){ // 全部埋め込む vector> imos(H + 1, vector(W + 1)); rep(i,H-K+1)rep(j,W-K+1){ imos[i][j]++; imos[i + K][j + K]++; imos[i + K][j]--; imos[i][j + K]--; } rep(i,H)rep(j,W)imos[i][j+1]+=imos[i][j]; rep(i,H)rep(j,W)imos[i+1][j]+=imos[i][j]; rep(i,H)rep(j,W)ans -= (mint(1) - mint(imos[i][j]) / (mint(H - K + 1) * mint(W - K + 1))).pow(N); } if (H < 2 * K && W >= 2 * K){ vector> imos(H + 1, vector(2 * K)); rep(i,H-K+1)rep(j,K){ debug(i, j); imos[i][j]++; imos[i + K][j + K]++; imos[i + K][j]--; imos[i][j + K]--; } rep(i,H)rep(j,K)imos[i][j+1]+=imos[i][j]; rep(i,H)rep(j,K)imos[i+1][j]+=imos[i][j]; // 両端 rep(i,H)rep(j,K)ans -= mint(2) * (mint(1) - mint(imos[i][j]) / (mint(H - K + 1) * mint(W - K + 1))).pow(N); rep(i,H)ans -= mint(W - 2 * K) * (mint(1) - mint(imos[i][K - 1]) / (mint(H - K + 1) * mint(W - K + 1))).pow(N); } if (H >= 2 * K && W >= 2 * K){ vector> imos(2 * K, vector(2 * K)); rep(i,K)rep(j,K){ imos[i][j]++; imos[i + K][j + K]++; imos[i + K][j]--; imos[i][j + K]--; } rep(i,K)rep(j,K)imos[i][j+1]+=imos[i][j]; rep(i,K)rep(j,K)imos[i+1][j]+=imos[i][j]; // 四隅 rep(i,K)rep(j,K)ans -= mint(4) * (mint(1) - mint(imos[i][j]) / (mint(H - K + 1) * mint(W - K + 1))).pow(N); // 棒 rep(i,K)ans -= mint(2 * W + 2 * H - 8 * K) * (mint(1) - mint((i + 1) * K) / (mint(H - K + 1) * mint(W - K + 1))).pow(N); ans -= mint(H - 2 * K) * mint(W - 2 * K) * (mint(1) - mint(K * K) / (mint(H - K + 1) * mint(W - K + 1))).pow(N); } cout << ans << endl; }