#include #define FASTIO using namespace std; using ll = long long; using Vi = std::vector; using Vl = std::vector; using Pii = std::pair; using Pll = std::pair; template using min_priority_queue = std::priority_queue, std::greater>; constexpr int I_INF = std::numeric_limits::max(); constexpr ll L_INF = std::numeric_limits::max(); template inline bool chmin(T1& a, const T2& b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, const T2& b) { if (a < b) { a = b; return true; } return false; } template class Prints { private: class __Prints { public: __Prints(const char* sep, const char* term) : sep(sep), term(term) {} template #if __cplusplus >= 201703L auto operator()(const Args&... args) const -> decltype((os << ... << std::declval()), void()) { #else void operator()(const Args&... args) const { #endif print(args...); } template #if __cplusplus >= 201703L auto pvec(const T& vec, size_t sz) const -> decltype(os << std::declval()[0])>(), void()) { #else void pvec(const T& vec, size_t sz) const { #endif for (size_t i = 0; i < sz; i++) os << vec[i] << (i == sz - 1 ? term : sep); } template #if __cplusplus >= 201703L auto pmat(const T& mat, size_t h, size_t w) const -> decltype(os << std::declval()[0][0])>(), void()) { #else void pmat(const T& mat, size_t h, size_t w) const { #endif for (size_t i = 0; i < h; i++) for (size_t j = 0; j < w; j++) os << mat[i][j] << (j == w - 1 ? term : sep); } private: const char *sep, *term; void print() const { os << term; } void print_rest() const { os << term; } template void print(const T& head, const Tail&... tail) const { os << head, print_rest(tail...); } template void print_rest(const T& head, const Tail&... tail) const { os << sep << head, print_rest(tail...); } }; public: Prints() {} __Prints operator()(const char* sep = " ", const char* term = "\n") const { return __Prints(sep, term); } }; Prints<> prints; Prints prints_err; //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% void solve() { ll A, B, C, N; cin >> A >> B >> C >> N; using Ti = tuple; using Td = tuple; map memo; auto dfs = [&](auto&& self, int n1, int n2, int n3, int k) -> Td { if (auto itr = memo.find({n1, n2, n3, k}); itr != memo.end()) { return itr->second; } if (k == N) { return {0.0, 0.0, 0.0}; } double r1 = 0.0, r2 = 0.0, r3 = 0.0; ll q = (n1 + n2 + n3) * (n1 + n2 + n3 - 1) / 2; if (n1 >= 2) { auto [t1, t2, t3] = self(self, n1 - 1, n2, n3, k + 1); ll p = n1 * (n1 - 1) / 2; r1 += (t1 + 1) * p; r2 += t2 * p; r3 += t3 * p; } if (n2 >= 2) { auto [t1, t2, t3] = self(self, n1, n2 - 1, n3, k + 1); ll p = n2 * (n2 - 1) / 2; r1 += t1 * p; r2 += (t2 + 1) * p; r3 += t3 * p; } if (n3 >= 2) { auto [t1, t2, t3] = self(self, n1, n2, n3 - 1, k + 1); ll p = n3 * (n3 - 1) / 2; r1 += t1 * p; r2 += t2 * p; r3 += (t3 + 1) * p; } { auto [t1, t2, t3] = self(self, n1, n2, n3, k + 1); ll p = n1 * n2 + n1 * n3 + n2 * n3; r1 += t1 * p; r2 += t2 * p; r3 += t3 * p; } return memo[{n1, n2, n3, k}] = {r1 / q, r2 / q, r3 / q}; }; auto [a1, a2, a3] = dfs(dfs, A, B, C, 0); prints()(a1, a2, a3); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% int main() { #ifdef FASTIO std::cin.tie(nullptr), std::cout.tie(nullptr); std::ios::sync_with_stdio(false); #endif #ifdef FILEINPUT std::ifstream ifs("./in_out/input.txt"); std::cin.rdbuf(ifs.rdbuf()); #endif #ifdef FILEOUTPUT std::ofstream ofs("./in_out/output.txt"); std::cout.rdbuf(ofs.rdbuf()); #endif std::cout << std::setprecision(18) << std::fixed; solve(); std::cout << std::flush; return 0; }