#line 2 "template.hpp" // #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #include using namespace std; template concept Streamable = requires(ostream os, T &x) { os << x; }; template concept is_modint = requires(mint &x) { { x.val() } -> std::convertible_to; }; #ifdef LOCAL #include #else #define debug(...) #endif template void print_one(const T &value) { cout << value; } template void print_one(const T &value) { cout << value.val(); } void print() { cout << '\n'; } template void print(const T &a, const Ts &...b) { print_one(a); ((cout << ' ', print_one(b)), ...); cout << '\n'; } template requires(!Streamable) void print(const Iterable &v) { for(auto it = v.begin(); it != v.end(); ++it) { if(it != v.begin()) cout << " "; print_one(*it); } cout << '\n'; } using ll = long long; using vl = vector; using vll = vector; using P = pair; #define all(v) v.begin(), v.end() #define UNIQUE(v) ranges::sort(v), v.erase(unique(all(v)), end(v)) template inline bool chmax(T &a, T b) { return ((a < b) ? (a = b, true) : (false)); } template inline bool chmin(T &a, T b) { return ((a > b) ? (a = b, true) : (false)); } // https://trap.jp/post/1224/ template constexpr auto min(T... a) { return min(initializer_list>{a...}); } template constexpr auto max(T... a) { return max(initializer_list>{a...}); } template void input(T &...a) { (cin >> ... >> a); } template void input(vector &a) { for(T &x : a) cin >> x; } #define INT(...) \ int __VA_ARGS__; \ input(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ input(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ input(__VA_ARGS__) #define REP1(a) for(ll i = 0; i < a; i++) #define REP2(i, a) for(ll i = 0; i < a; i++) #define REP3(i, a, b) for(ll i = a; i < b; i++) #define REP4(i, a, b, c) for(ll i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__) #define rep1(i, n) for(ll i = 1; i <= ((ll)n); ++i) ll inf = 3e18; vl dx = {1, -1, 0, 0}; vl dy = {0, 0, 1, -1}; #line 2 "/home/y_midori/cp/a.cpp" #include using mint = atcoder::modint998244353; void solve() { INT(h, w, n, k); mint ans = 0; int imax = min(k, h - k), jmax = min(k, w - k); mint linv = mint(mint(h - k + 1) * (w - k + 1)).inv(); // 四隅 for(int i = 1; i <= imax; ++i) { for(int j = 1; j <= jmax; ++j) { mint p = 1 - linv * i * j; ans += 4 * (1 - p.pow(n)); } } mint hl = abs(h - 2 * k), wl = abs(w - 2 * k); mint hr = (h >= 2 * k ? k : h - k + 1), wr = (w >= 2 * k ? k : w - k + 1); // 中 mint p = 1 - linv * hr * wr; ans += hl * wl * (1 - p.pow(n)); // 上下 for(int i = 1; i <= imax; ++i) { mint p = 1 - linv * i * wr; ans += 2 * wl * (1 - p.pow(n)); } // 左右 for(int j = 1; j <= jmax; ++j) { mint p = 1 - linv * j * hr; ans += 2 * hl * (1 - p.pow(n)); } print(ans); } int main() { solve(); }