#define LOCAL #define _USE_MATH_DEFINES #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; template ostream& operator <<(ostream& out, const pair& a) { out << "(" << a.first << "," << a.second << ")"; return out; } template ostream& operator <<(ostream& out, const array& a) { out << "["; bool first = true; for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]"; return out; } template ostream& operator <<(ostream& out, const vector& a) { out << "["; bool first = true; for (auto v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]"; return out; } template ostream& operator <<(ostream& out, const set& a) { out << "{"; bool first = true; for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}"; return out; } template ostream& operator <<(ostream& out, const map& a) { out << "{"; bool first = true; for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}"; return out; } #ifdef LOCAL #define trace(...) __f(#__VA_ARGS__, __VA_ARGS__) #else #define trace(...) 42 #endif template void __f(const char* name, Arg1&& arg1){ cerr << name << ": " << arg1 << endl; } template void __f(const char* names, Arg1&& arg1, Args&&... args){ const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << ": " << arg1 << " |"; __f(comma + 1, args...); } template auto vect(const T& v, int n) { return vector(n, v); } template auto vect(const T& v, int n, D... m) { return vector(n, vect(v, m...)); } typedef long long int64; typedef pair ii; #define SZ(x) (int)((x).size()) template static constexpr T inf = numeric_limits::max() / 2; const int MOD = 1e9 + 7; // const int MOD = 998244353; mt19937 mrand(random_device{}()); int rnd(int x) { return mrand() % x; } // mt19937_64 mrand(random_device{}()); // int64 rnd(int64 x) { return mrand() % x; } template void out(const vector& a) { for (int i = 0; i < SZ(a); ++i) cout << a[i] << " \n"[i + 1 == SZ(a)]; } template bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } template void dedup(vector& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); } void add(int& x, int y) { x += y; if (x >= MOD) x -= MOD; } struct fast_ios { fast_ios() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); }; } fast_ios_; array operator +(const array& lhs, const array& rhs) { return {lhs[0] + rhs[0], lhs[1] + rhs[1], lhs[2] + rhs[2]}; } array operator *(const double x, const array& v) { return {x * v[0], x * v[1], x * v[2]}; } int main() { int a, b, c, n; cin >> a >> b >> c >> n; const int N = 50 + 10; auto dp = vect>({-1, -1, -1}, N, N, N, N); auto C2 = [&](int x) { return 1.0 * x * (x - 1); }; function(int, int, int, int)> solve = [&](int x, int y, int z, int rem) { int m = x + y + z; if (rem == 0 || m < 2) return array{0, 0, 0}; auto& ret = dp[x][y][z][rem]; if (ret[0] > -0.5) return ret; double px = C2(x) / C2(m); double py = C2(y) / C2(m); double pz = C2(z) / C2(m); double q = 1 - px - py - pz; // trace(x, y, z, px, py, pz, q); ret = {0, 0, 0}; if (x >= 2) ret = ret + px * solve(x - 1, y, z, rem - 1) + array{px, 0.0, 0.0}; if (y >= 2) ret = ret + py * solve(x, y - 1, z, rem - 1) + array{0.0, py, 0.0}; if (z >= 2) ret = ret + pz * solve(x, y, z - 1, rem - 1) + array{0.0, 0.0, pz}; ret = ret + q * solve(x, y, z, rem - 1); return ret; }; auto ret = solve(a, b, c, n); cout << ret[0] << " " << ret[1] << " " << ret[2] << '\n'; return 0; }